diff --git a/clang/lib/CodeGen/CGOpenMPRuntime.cpp b/clang/lib/CodeGen/CGOpenMPRuntime.cpp
--- a/clang/lib/CodeGen/CGOpenMPRuntime.cpp
+++ b/clang/lib/CodeGen/CGOpenMPRuntime.cpp
@@ -10377,7 +10377,9 @@
     }
     Linkage = CGM.getLLVMLinkageVarDefinition(VD, /*IsConstant=*/false);
     // Temp solution to prevent optimizations of the internal variables.
-    if (CGM.getLangOpts().OpenMPIsDevice && !VD->isExternallyVisible()) {
+    if (CGM.getLangOpts().OpenMPIsDevice &&
+        (!VD->isExternallyVisible() ||
+         Linkage == llvm::GlobalValue::LinkOnceODRLinkage)) {
       // Do not create a "ref-variable" if the original is not also available
       // on the host.
       if (!OffloadEntriesInfoManager.hasDeviceGlobalVarEntryInfo(VarName))
diff --git a/openmp/libomptarget/test/offloading/target_constexpr_mapping.cpp b/openmp/libomptarget/test/offloading/target_constexpr_mapping.cpp
new file mode 100644
--- /dev/null
+++ b/openmp/libomptarget/test/offloading/target_constexpr_mapping.cpp
@@ -0,0 +1,34 @@
+// RUN: %libomptarget-compileoptxx-run-and-check-generic
+
+#include <omp.h>
+#include <stdio.h>
+
+#pragma omp declare target
+class A {
+public:
+  constexpr static double pi = 3.141592653589793116;
+  A() { ; }
+  ~A() { ; }
+};
+#pragma omp end declare target
+
+#pragma omp declare target
+constexpr static double anotherPi = 3.14;
+#pragma omp end declare target
+
+int main() {
+  double a[2];
+#pragma omp target map(tofrom : a[:2])
+  {
+    a[0] = A::pi;
+    a[1] = anotherPi;
+  }
+
+  // CHECK: pi = 3.141592653589793116
+  printf("pi = %.18f\n", a[0]);
+
+  // CHECK: anotherPi = 3.14
+  printf("anotherPi = %.2f\n", a[1]);
+
+  return 0;
+}