diff --git a/llvm/include/llvm/Transforms/IPO/Attributor.h b/llvm/include/llvm/Transforms/IPO/Attributor.h
--- a/llvm/include/llvm/Transforms/IPO/Attributor.h
+++ b/llvm/include/llvm/Transforms/IPO/Attributor.h
@@ -1599,6 +1599,19 @@
   ///
   static void createShallowWrapper(Function &F);
 
+  /// Make another copy of the function \p F such that the copied version has
+  /// internal linkage afterwards and can be analysed. Then we replace all uses
+  /// of the original function to the copied one
+  ///
+  /// Only non-exactly defined functions that have `linkonce_odr` or `weak_odr`
+  /// linkage can be internalized because these linkages guarantee that other
+  /// definitions with the same name have the same semantics as this one
+  ///
+  /// This will only be run if the `attributor-allow-deep-wrappers` option is
+  /// set, or if the function is called with \p Force set to true.
+  ///
+  static Function *internalizeFunction(Function &F, bool Force = false);
+
   /// Return the data layout associated with the anchor scope.
   const DataLayout &getDataLayout() const { return InfoCache.DL; }
 
diff --git a/llvm/lib/Transforms/IPO/Attributor.cpp b/llvm/lib/Transforms/IPO/Attributor.cpp
--- a/llvm/lib/Transforms/IPO/Attributor.cpp
+++ b/llvm/lib/Transforms/IPO/Attributor.cpp
@@ -1527,19 +1527,12 @@
   NumFnShallowWrappersCreated++;
 }
 
-/// Make another copy of the function \p F such that the copied version has
-/// internal linkage afterwards and can be analysed. Then we replace all uses
-/// of the original function to the copied one
-///
-/// Only non-exactly defined functions that have `linkonce_odr` or `weak_odr`
-/// linkage can be internalized because these linkages guarantee that other
-/// definitions with the same name have the same semantics as this one
-///
-static Function *internalizeFunction(Function &F) {
-  assert(AllowDeepWrapper && "Cannot create a copy if not allowed.");
-  assert(!F.isDeclaration() && !F.hasExactDefinition() &&
-         !GlobalValue::isInterposableLinkage(F.getLinkage()) &&
-         "Trying to internalize function which cannot be internalized.");
+Function *Attributor::internalizeFunction(Function &F, bool Force) {
+  if (!AllowDeepWrapper && !Force)
+    return nullptr;
+  if (F.isDeclaration() || F.hasLocalLinkage() ||
+      GlobalValue::isInterposableLinkage(F.getLinkage()))
+    return nullptr;
 
   Module &M = *F.getParent();
   FunctionType *FnTy = F.getFunctionType();
@@ -2354,7 +2347,8 @@
       Function *F = Functions[u];
       if (!F->isDeclaration() && !F->isDefinitionExact() && F->getNumUses() &&
           !GlobalValue::isInterposableLinkage(F->getLinkage())) {
-        Function *NewF = internalizeFunction(*F);
+        Function *NewF = Attributor::internalizeFunction(*F);
+        assert(NewF && "Could not internalize function.");
         Functions.insert(NewF);
 
         // Update call graph
diff --git a/llvm/lib/Transforms/IPO/OpenMPOpt.cpp b/llvm/lib/Transforms/IPO/OpenMPOpt.cpp
--- a/llvm/lib/Transforms/IPO/OpenMPOpt.cpp
+++ b/llvm/lib/Transforms/IPO/OpenMPOpt.cpp
@@ -2564,11 +2564,18 @@
   if (DisableOpenMPOptimizations)
     return PreservedAnalyses::all();
 
+  // Create internal copies of each function if this is a kernel Module.
+  if (!OMPInModule.getKernels().empty())
+    for (Function &F : M)
+      if (!F.isDeclaration() && F.hasExternalLinkage() &&
+          !OMPInModule.getKernels().contains(&F))
+        Attributor::internalizeFunction(F, /* Force */ true);
+
   // Look at every function definition in the Module.
   SmallVector<Function *, 16> SCC;
-  for (Function &Fn : M)
-    if (!Fn.isDeclaration())
-      SCC.push_back(&Fn);
+  for (Function &F : M)
+    if (!F.isDeclaration())
+      SCC.push_back(&F);
 
   if (SCC.empty())
     return PreservedAnalyses::all();
diff --git a/llvm/test/Transforms/OpenMP/single_threaded_execution.ll b/llvm/test/Transforms/OpenMP/single_threaded_execution.ll
--- a/llvm/test/Transforms/OpenMP/single_threaded_execution.ll
+++ b/llvm/test/Transforms/OpenMP/single_threaded_execution.ll
@@ -1,8 +1,8 @@
-; RUN: opt -passes=openmp-opt-cgscc -debug-only=openmp-opt -disable-output < %s 2>&1 | FileCheck %s
+; RUN: opt -passes=openmp-opt -debug-only=openmp-opt -disable-output < %s 2>&1 | FileCheck %s
 ; REQUIRES: asserts
 ; ModuleID = 'single_threaded_exeuction.c'
 
-define void @kernel() {
+define weak void @kernel() {
   call void @__kmpc_kernel_init(i32 512, i16 1)
   call void @nvptx()
   call void @amdgcn()
@@ -12,7 +12,7 @@
 ; CHECK-NOT: [openmp-opt] Basic block @nvptx entry is executed by a single thread.
 ; CHECK: [openmp-opt] Basic block @nvptx if.then is executed by a single thread.
 ; CHECK-NOT: [openmp-opt] Basic block @nvptx if.end is executed by a single thread.
-; Function Attrs: noinline nounwind uwtable
+; Function Attrs: noinline
 define dso_local void @nvptx() {
 entry:
   %call = call i32 @llvm.nvvm.read.ptx.sreg.tid.x()
@@ -20,6 +20,7 @@
   br i1 %cmp, label %if.then, label %if.end
 
 if.then:
+  call void @foo()
   call void @bar()
   br label %if.end
 
@@ -30,7 +31,7 @@
 ; CHECK-NOT: [openmp-opt] Basic block @amdgcn entry is executed by a single thread.
 ; CHECK: [openmp-opt] Basic block @amdgcn if.then is executed by a single thread.
 ; CHECK-NOT: [openmp-opt] Basic block @amdgcn if.end is executed by a single thread.
-; Function Attrs: noinline nounwind uwtable
+; Function Attrs: noinline
 define dso_local void @amdgcn() {
 entry:
   %call = call i32 @llvm.amdgcn.workitem.id.x()
@@ -38,6 +39,7 @@
   br i1 %cmp, label %if.then, label %if.end
 
 if.then:
+  call void @foo()
   call void @bar()
   br label %if.end
 
@@ -45,9 +47,16 @@
   ret void
 }
 
-; CHECK: [openmp-opt] Basic block @bar entry is executed by a single thread.
-; Function Attrs: noinline nounwind uwtable
-define internal void @bar() {
+; CHECK: [openmp-opt] Basic block @foo entry is executed by a single thread.
+; Function Attrs: noinline
+define internal void @foo() {
+entry:
+  ret void
+}
+
+; CHECK: [openmp-opt] Basic block @bar.internalized entry is executed by a single thread.
+; Function Attrs: noinline
+define void @bar() {
 entry:
   ret void
 }