diff --git a/blas/tpls/KokkosBlas1_nrm1_tpl_spec_avail.hpp b/blas/tpls/KokkosBlas1_nrm1_tpl_spec_avail.hpp
index be0a45c7be..8f79c8a58d 100644
--- a/blas/tpls/KokkosBlas1_nrm1_tpl_spec_avail.hpp
+++ b/blas/tpls/KokkosBlas1_nrm1_tpl_spec_avail.hpp
@@ -116,8 +116,7 @@ KOKKOSBLAS1_NRM1_TPL_SPEC_AVAIL_ROCBLAS(Kokkos::complex<float>,
 // oneMKL
 #ifdef KOKKOSKERNELS_ENABLE_TPL_MKL
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 
 #define KOKKOSBLAS1_NRM1_TPL_SPEC_AVAIL_MKL_SYCL(SCALAR, LAYOUT, MEMSPACE)     \
   template <class ExecSpace>                                                   \
diff --git a/blas/tpls/KokkosBlas1_nrm1_tpl_spec_decl.hpp b/blas/tpls/KokkosBlas1_nrm1_tpl_spec_decl.hpp
index c695eaee1e..12a240db6b 100644
--- a/blas/tpls/KokkosBlas1_nrm1_tpl_spec_decl.hpp
+++ b/blas/tpls/KokkosBlas1_nrm1_tpl_spec_decl.hpp
@@ -334,8 +334,7 @@ KOKKOSBLAS1_NRM1_TPL_SPEC_DECL_ROCBLAS(Kokkos::complex<double>,
 // oneMKL
 #ifdef KOKKOSKERNELS_ENABLE_TPL_MKL
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 
 #include <KokkosBlas_tpl_spec.hpp>
 #include <oneapi/mkl/blas.hpp>
diff --git a/blas/tpls/KokkosBlas1_nrm2_tpl_spec_avail.hpp b/blas/tpls/KokkosBlas1_nrm2_tpl_spec_avail.hpp
index de930f6107..7bc55becc0 100644
--- a/blas/tpls/KokkosBlas1_nrm2_tpl_spec_avail.hpp
+++ b/blas/tpls/KokkosBlas1_nrm2_tpl_spec_avail.hpp
@@ -88,9 +88,7 @@ KOKKOSBLAS1_NRM2_TPL_SPEC_AVAIL(Kokkos::LayoutLeft, Kokkos::HIP,
                                 Kokkos::HIPSpace)
 #endif
 
-#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) &&                \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE) && \
-    defined(KOKKOS_ENABLE_SYCL)
+#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) && defined(KOKKOS_ENABLE_SYCL)
 KOKKOSBLAS1_NRM2_TPL_SPEC_AVAIL(Kokkos::LayoutLeft, Kokkos::Experimental::SYCL,
                                 Kokkos::Experimental::SYCLDeviceUSMSpace)
 #endif
diff --git a/blas/tpls/KokkosBlas1_nrm2_tpl_spec_decl.hpp b/blas/tpls/KokkosBlas1_nrm2_tpl_spec_decl.hpp
index 736523aa8d..ef45238405 100644
--- a/blas/tpls/KokkosBlas1_nrm2_tpl_spec_decl.hpp
+++ b/blas/tpls/KokkosBlas1_nrm2_tpl_spec_decl.hpp
@@ -364,9 +364,7 @@ KOKKOSBLAS1_NRM2_TPL_SPEC_DECL_ROCBLAS_EXT(false)
 
 #endif
 
-#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) &&                \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE) && \
-    defined(KOKKOS_ENABLE_SYCL)
+#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) && defined(KOKKOS_ENABLE_SYCL)
 #include <mkl.h>
 #include <oneapi/mkl/blas.hpp>
 #include <KokkosBlas_tpl_spec.hpp>
diff --git a/blas/tpls/KokkosBlas2_gemv_tpl_spec_avail.hpp b/blas/tpls/KokkosBlas2_gemv_tpl_spec_avail.hpp
index 0820badd9a..661393e445 100644
--- a/blas/tpls/KokkosBlas2_gemv_tpl_spec_avail.hpp
+++ b/blas/tpls/KokkosBlas2_gemv_tpl_spec_avail.hpp
@@ -161,8 +161,7 @@ KOKKOSBLAS2_GEMV_TPL_SPEC_AVAIL_ROCBLAS(Kokkos::complex<float>,
 
 #ifdef KOKKOSKERNELS_ENABLE_TPL_MKL
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 
 #define KOKKOSBLAS2_GEMV_TPL_SPEC_AVAIL_ONEMKL(SCALAR, LAYOUT)               \
   template <class ExecSpace>                                                 \
diff --git a/blas/tpls/KokkosBlas2_gemv_tpl_spec_decl.hpp b/blas/tpls/KokkosBlas2_gemv_tpl_spec_decl.hpp
index 2ace065808..304dd349bf 100644
--- a/blas/tpls/KokkosBlas2_gemv_tpl_spec_decl.hpp
+++ b/blas/tpls/KokkosBlas2_gemv_tpl_spec_decl.hpp
@@ -767,9 +767,7 @@ KOKKOSBLAS2_CGEMV_ROCBLAS(Kokkos::LayoutRight, Kokkos::HIPSpace, false)
 #endif  // KOKKOSKERNELS_ENABLE_TPL_ROCBLAS
 
 // ONEMKL
-#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) &&                \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE) && \
-    defined(KOKKOS_ENABLE_SYCL)
+#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) && defined(KOKKOS_ENABLE_SYCL)
 #include <mkl.h>
 #include <oneapi/mkl/blas.hpp>
 #include <KokkosBlas_tpl_spec.hpp>
diff --git a/blas/tpls/KokkosBlas_Host_tpl.hpp b/blas/tpls/KokkosBlas_Host_tpl.hpp
index d28f7a2186..f7fb3d3978 100644
--- a/blas/tpls/KokkosBlas_Host_tpl.hpp
+++ b/blas/tpls/KokkosBlas_Host_tpl.hpp
@@ -32,7 +32,7 @@
 namespace KokkosBlas {
 namespace Impl {
 
-#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL)
+#if defined(KOKKOSKERNELS_ENABLE_TPL_MKL) && defined(MKL_PROVIDES_BLAS_LAPACK)
 using KK_INT = MKL_INT;
 #else
 using KK_INT = int;
diff --git a/cmake/KokkosKernels_config.h.in b/cmake/KokkosKernels_config.h.in
index ef8fea78b8..9f6a0b85d5 100644
--- a/cmake/KokkosKernels_config.h.in
+++ b/cmake/KokkosKernels_config.h.in
@@ -29,7 +29,6 @@
    requires (a) header file(s) as well, and may use functions other
    than just BLAS and LAPACK functions.  */
 #cmakedefine HAVE_KOKKOSKERNELS_MKL
-#cmakedefine KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE
 
 #cmakedefine KOKKOSKERNELS_ENABLE_TESTS_AND_PERFSUITE
 #cmakedefine KOKKOSKERNELS_ENABLE_BENCHMARK
@@ -154,6 +153,9 @@
 #endif
 #endif
 
+/* Whether MKL is providing the BLAS and LAPACK implementation */
+#cmakedefine MKL_PROVIDES_BLAS_LAPACK
+
 #if !defined(KOKKOS_ENABLE_CUDA) && !defined(KOKKOS_ENABLE_HIP) && \
     !defined(KOKKOS_ENABLE_SYCL) && !defined(KOKKOS_ENABLE_OPENMPTARGET)
 #define KOKKOSKERNELS_ENABLE_HOST_ONLY
diff --git a/cmake/Modules/FindTPLBLAS.cmake b/cmake/Modules/FindTPLBLAS.cmake
index 0bc73fc73f..67e4cc9a08 100644
--- a/cmake/Modules/FindTPLBLAS.cmake
+++ b/cmake/Modules/FindTPLBLAS.cmake
@@ -8,4 +8,3 @@ ELSE()
   FIND_PACKAGE(BLAS REQUIRED)
   KOKKOSKERNELS_CREATE_IMPORTED_TPL(BLAS INTERFACE LINK_LIBRARIES ${BLAS_LIBRARIES})
 ENDIF()
-
diff --git a/cmake/Modules/FindTPLLAPACK.cmake b/cmake/Modules/FindTPLLAPACK.cmake
index 463f61afeb..f6d345d5ee 100644
--- a/cmake/Modules/FindTPLLAPACK.cmake
+++ b/cmake/Modules/FindTPLLAPACK.cmake
@@ -8,4 +8,3 @@ ELSE()
   FIND_PACKAGE(LAPACK REQUIRED)
   KOKKOSKERNELS_CREATE_IMPORTED_TPL(LAPACK INTERFACE LINK_LIBRARIES ${LAPACK_LIBRARIES})
 ENDIF()
-
diff --git a/cmake/Modules/FindTPLMKL.cmake b/cmake/Modules/FindTPLMKL.cmake
index 52f4571976..1ecd882e71 100644
--- a/cmake/Modules/FindTPLMKL.cmake
+++ b/cmake/Modules/FindTPLMKL.cmake
@@ -74,3 +74,7 @@ ELSE()
     )
     ENDIF()
 ENDIF()
+# This logic to find MKL is only used in non-Trilinos builds.
+# In this case, MKL can always be used as the host BLAS/LAPACK implementation
+# (whether MKL_INT is 32- or 64-bit).
+set (MKL_PROVIDES_BLAS_LAPACK ON INTERNAL)
diff --git a/cmake/kokkoskernels_tpls.cmake b/cmake/kokkoskernels_tpls.cmake
index d1a44721e6..6af952ce94 100644
--- a/cmake/kokkoskernels_tpls.cmake
+++ b/cmake/kokkoskernels_tpls.cmake
@@ -31,10 +31,6 @@ MACRO(KOKKOSKERNELS_ADD_TPL_OPTION NAME DEFAULT_VALUE DOCSTRING)
   SET(ROOT_DEFAULT $ENV{${_NAME_ORIG}_ROOT})
   KOKKOSKERNELS_ADD_OPTION(${_NAME_ORIG}_ROOT "${ROOT_DEFAULT}" PATH "Location of ${_NAME} install root. Default: None or the value of the environment variable ${_NAME}_ROOT if set")
   IF (DEFINED TPL_ENABLE_${_NAME})
-    IF (${_NAME} STREQUAL MKL AND KOKKOSKERNELS_HAS_TRILINOS)
-      MESSAGE("Trilinos has enabled MKL and SYCL but it does not detect oneMKL correctly so we disable it!")
-      SET(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE ON)
-    ENDIF ()
     IF (TPL_ENABLE_${_NAME} AND NOT KOKKOSKERNELS_ENABLE_TPL_${_NAME})
       MESSAGE("Overriding KOKKOSKERNELS_ENABLE_TPL_${_NAME_ORIG}=OFF with TPL_ENABLE_${_NAME}=ON")
       SET(KOKKOSKERNELS_ENABLE_TPL_${_NAME_ORIG} ON)
diff --git a/sparse/src/KokkosSparse_spmv_handle.hpp b/sparse/src/KokkosSparse_spmv_handle.hpp
index a2eecfd1ce..b3e878b5e9 100644
--- a/sparse/src/KokkosSparse_spmv_handle.hpp
+++ b/sparse/src/KokkosSparse_spmv_handle.hpp
@@ -189,8 +189,7 @@ struct MKL_SpMV_Data : public TPL_SpMV_Data<ExecutionSpace> {
 };
 #endif
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 struct OneMKL_SpMV_Data : public TPL_SpMV_Data<Kokkos::Experimental::SYCL> {
   OneMKL_SpMV_Data(const Kokkos::Experimental::SYCL& exec_)
       : TPL_SpMV_Data(exec_) {}
diff --git a/sparse/tpls/KokkosSparse_spmv_tpl_spec_avail.hpp b/sparse/tpls/KokkosSparse_spmv_tpl_spec_avail.hpp
index 854c2f2b26..881352d950 100644
--- a/sparse/tpls/KokkosSparse_spmv_tpl_spec_avail.hpp
+++ b/sparse/tpls/KokkosSparse_spmv_tpl_spec_avail.hpp
@@ -257,8 +257,7 @@ KOKKOSSPARSE_SPMV_TPL_SPEC_AVAIL_MKL(Kokkos::complex<float>, Kokkos::OpenMP)
 KOKKOSSPARSE_SPMV_TPL_SPEC_AVAIL_MKL(Kokkos::complex<double>, Kokkos::OpenMP)
 #endif
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 #define KOKKOSSPARSE_SPMV_TPL_SPEC_AVAIL_ONEMKL(SCALAR, ORDINAL, MEMSPACE)     \
   template <>                                                                  \
   struct spmv_tpl_spec_avail<                                                  \
diff --git a/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp b/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
index 1555050420..66ea90c746 100644
--- a/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
+++ b/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
@@ -678,8 +678,7 @@ KOKKOSSPARSE_SPMV_MKL(Kokkos::complex<double>, Kokkos::OpenMP)
 #undef KOKKOSSPARSE_SPMV_MKL
 #endif
 
-#if defined(KOKKOS_ENABLE_SYCL) && \
-    !defined(KOKKOSKERNELS_ENABLE_TPL_MKL_SYCL_OVERRIDE)
+#if defined(KOKKOS_ENABLE_SYCL)
 inline oneapi::mkl::transpose mode_kk_to_onemkl(char mode_kk) {
   switch (toupper(mode_kk)) {
     case 'N': return oneapi::mkl::transpose::nontrans;