How to conditional set up a Makefile variable by testing if a file exists

For example: I want:

if file1 exists:

CLEAN_SRC = *.h file3

else

CLEAN_SRC = 

If file1 does not exist then $(wildcard file1) will evaluate to an empty string.

ifeq ($(wildcard file1),) 
    CLEAN_SRC =
else 
    CLEAN_SRC = *.h file3
endif