diff --git a/src/plugins/intel_cpu/CMakeLists.txt b/src/plugins/intel_cpu/CMakeLists.txt
index 49a9c2991c1c62..aa6ce49a051e00 100644
--- a/src/plugins/intel_cpu/CMakeLists.txt
+++ b/src/plugins/intel_cpu/CMakeLists.txt
@@ -280,8 +280,8 @@ target_include_directories(${TARGET_NAME} PRIVATE $<TARGET_PROPERTY:openvino::re
 
 # ARCH lists for softmax.cpp and mha_single_token.cpp
 # Based on result of above calls, decide whether to add SVE
-set(SOFTMAX_ARCH_LIST           AVX512F AVX2 ANY)
-set(MHA_SINGLE_TOKEN_ARCH_LIST  AVX512F AVX2 ANY)
+set(SOFTMAX_ARCH_LIST           AVX512F AVX2)
+set(MHA_SINGLE_TOKEN_ARCH_LIST  AVX512F AVX2)
 
 if(ENABLE_NEON_FP16)
     list(APPEND SOFTMAX_ARCH_LIST NEON_FP16)
@@ -293,6 +293,9 @@ if(ENABLE_SVE)
     list(APPEND MHA_SINGLE_TOKEN_ARCH_LIST SVE)
 endif()
 
+list(APPEND SOFTMAX_ARCH_LIST ANY)
+list(APPEND MHA_SINGLE_TOKEN_ARCH_LIST ANY)
+
 # Cross compiled function
 # TODO: The same for proposal, proposalONNX, topk
 cross_compiled_file(${TARGET_NAME}