diff --git a/Modules/FindCUDAToolkit.cmake b/Modules/FindCUDAToolkit.cmake
index aaa1246663..8c7916cdf9 100644
--- a/Modules/FindCUDAToolkit.cmake
+++ b/Modules/FindCUDAToolkit.cmake
@@ -939,13 +939,25 @@ endif()
 
 # Find target directory when crosscompiling.
 if(CMAKE_CROSSCOMPILING)
+  # When a language is enabled we can use its compiler's target architecture.
+  if(CMAKE_CUDA_COMPILER_LOADED AND CMAKE_CUDA_COMPILER_ARCHITECTURE_ID)
+    set(_CUDA_TARGET_PROCESSOR "${CMAKE_CUDA_COMPILER_ARCHITECTURE_ID}")
+  elseif(CMAKE_CXX_COMPILER_LOADED AND CMAKE_CXX_COMPILER_ARCHITECTURE_ID)
+    set(_CUDA_TARGET_PROCESSOR "${CMAKE_CXX_COMPILER_ARCHITECTURE_ID}")
+  elseif(CMAKE_C_COMPILER_LOADED AND CMAKE_C_COMPILER_ARCHITECTURE_ID)
+    set(_CUDA_TARGET_PROCESSOR "${CMAKE_C_COMPILER_ARCHITECTURE_ID}")
+  elseif(CMAKE_SYSTEM_PROCESSOR)
+    set(_CUDA_TARGET_PROCESSOR "${CMAKE_SYSTEM_PROCESSOR}")
+  else()
+    message(FATAL_ERROR "Cross-compiling with the CUDA toolkit requires CMAKE_SYSTEM_PROCESSOR to be set.")
+  endif()
   # Keep in sync with equivalent table in CMakeDetermineCUDACompiler and FindCUDA!
-  if(CMAKE_SYSTEM_PROCESSOR STREQUAL "armv7-a")
+  if(_CUDA_TARGET_PROCESSOR STREQUAL "armv7-a")
     # Support for NVPACK
     set(CUDAToolkit_TARGET_NAMES "armv7-linux-androideabi")
-  elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "arm")
+  elseif(_CUDA_TARGET_PROCESSOR MATCHES "arm")
     set(CUDAToolkit_TARGET_NAMES "armv7-linux-gnueabihf")
-  elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "aarch64")
+  elseif(_CUDA_TARGET_PROCESSOR MATCHES "aarch64")
     if(ANDROID_ARCH_NAME STREQUAL "arm64")
       set(CUDAToolkit_TARGET_NAMES "aarch64-linux-androideabi")
     elseif (CMAKE_SYSTEM_NAME STREQUAL "QNX")
@@ -953,9 +965,10 @@ if(CMAKE_CROSSCOMPILING)
     else()
       set(CUDAToolkit_TARGET_NAMES "aarch64-linux" "sbsa-linux")
     endif()
-  elseif(CMAKE_SYSTEM_PROCESSOR STREQUAL "x86_64")
+  elseif(_CUDA_TARGET_PROCESSOR STREQUAL "x86_64")
     set(CUDAToolkit_TARGET_NAMES "x86_64-linux")
   endif()
+  unset(_CUDA_TARGET_PROCESSOR)
 
   foreach(CUDAToolkit_TARGET_NAME IN LISTS CUDAToolkit_TARGET_NAMES)
     if(EXISTS "${CUDAToolkit_ROOT_DIR}/targets/${CUDAToolkit_TARGET_NAME}")