diff --git a/cmake/modules/openmp.cmake b/cmake/modules/openmp.cmake
index 87fc327c4..3d9e55c62 100644
--- a/cmake/modules/openmp.cmake
+++ b/cmake/modules/openmp.cmake
@@ -4,21 +4,40 @@ option(USE_OpenMP "Use OpenMP" ON)
 # This finds the library path from the system's clang for OpenMP
 #
 # On Fedora, it's at the same place as others, so we don't need to look elsewhere
-# On Ubuntu, it's in /usr/lib/llvm-${version}, so find_package finds GOMP for GCC instead.
-execute_process (
-    COMMAND bash -c "for lib in $(clang -lomp -### 2>&1); do echo $lib | grep -o \"\\/.*llvm.*\\w\"; done"
-    OUTPUT_VARIABLE LLVM_OMP_PATH
-)
-# Only if we found an "llvm" path that we need to add
-if (LLVM_OMP_PATH)
-  set(CMAKE_PREFIX_PATH ${LLVM_OMP_PATH})
-endif()
+# On Ubuntu, it's in /usr/lib/llvm-${version}, so GCC finds GOMP instead.
 
 if(USE_OpenMP)
-  find_package(OpenMP)
-  if(OPENMP_FOUND)
+  # Only bypass for GCC
+  if(CMAKE_CXX_COMPILER_ID STREQUAL "GNU")
+    # Only if we found an "llvm" path that we need to add
+    find_library(LLVM_OMP NAMES omp libomp libomp.so libomp.so.5)
+    find_library(PTHREAD NAMES pthread libpthread libpthread.a libpthread.so)
+    if (NOT LLVM_OMP OR NOT PTHREAD)
+      message(FATAL_ERROR "LLVM OpenMP required but not found")
+    endif()
+    set(OPENMP_FOUND ON)
+    set(OpenMP_C_FLAGS "-fopenmp")
+    set(OpenMP_C_LIBRARIES "${LLVM_OMP};${PTHREAD}")
+    set(OpenMP_C_LIB_NAMES "omp;pthread")
+
     message(STATUS "OpenMP found")
-  else()
-    message(FATAL_ERROR "OpenMP required but not found")
-  endif()
-endif()
+    message(STATUS "OpenMP C flags: ${OpenMP_C_FLAGS}")
+    message(STATUS "OpenMP C libs: ${OpenMP_C_LIBRARIES}")
+    message(STATUS "OpenMP C libnames: ${OpenMP_C_LIB_NAMES}")
+
+  else() # GNU / LLVM
+
+    # Clang always prefers its own OpenMP
+    find_package(OpenMP)
+    if(OPENMP_FOUND)
+      message(STATUS "OpenMP found")
+      message(STATUS "OpenMP version: ${OpenMP_C_VERSION}")
+      message(STATUS "OpenMP C flags: ${OpenMP_C_FLAGS}")
+      message(STATUS "OpenMP C libs: ${OpenMP_C_LIBRARIES}")
+      message(STATUS "OpenMP C libnames: ${OpenMP_C_LIB_NAMES}")
+    else()
+      message(FATAL_ERROR "LLVM OpenMP required but not found")
+    endif()
+
+  endif() # GNU / LLVM
+endif() # USE_OpenMP
diff --git a/cmake/modules/xsmm-dnn.cmake b/cmake/modules/xsmm-dnn.cmake
index 5a748788a..8057a7344 100644
--- a/cmake/modules/xsmm-dnn.cmake
+++ b/cmake/modules/xsmm-dnn.cmake
@@ -46,6 +46,6 @@ target_include_directories(xsmm_dnn_mlp PRIVATE ${XSMM_DNN_INCLUDE_DIRS})
 target_link_libraries(xsmm_dnn_mlp PRIVATE xsmm)
 if (OPENMP_FOUND)
   target_compile_options(xsmm_dnn_mlp PRIVATE ${OpenMP_C_FLAGS})
-  target_link_libraries(xsmm_dnn_mlp PRIVATE omp)
+  target_link_libraries(xsmm_dnn_mlp PRIVATE ${OpenMP_C_LIB_NAMES})
 endif()
 install(TARGETS xsmm_dnn_mlp RUNTIME DESTINATION bin)
diff --git a/tools/tpp-run/CMakeLists.txt b/tools/tpp-run/CMakeLists.txt
index 300be5d0d..791954d67 100644
--- a/tools/tpp-run/CMakeLists.txt
+++ b/tools/tpp-run/CMakeLists.txt
@@ -9,10 +9,6 @@ if(USE_OneDNN)
   set(ONEDNN_LIBS_INCL "-ltpp_dnnl_runner_utils")
 endif()
 
-if(USE_OpenMP)
-  set(OPENMP_LIBS_INCL "-lomp")
-endif()
-
 set(LIBS
         ${dialect_libs}
         ${conversion_libs}
@@ -81,7 +77,7 @@ target_link_options(tpp-run PRIVATE
   -lmlir_runner_utils
   -lmlir_async_runtime
   ${TPP_GPU_LINK_FLAGS}
-  ${OPENMP_LIBS_INCL}
+  $<$<BOOL:${USE_OpenMP}>:${OpenMP_C_LIBRARIES}>
   -Wl,--as-needed
 )