Borrowed from https://github.com/msys2-contrib/cpython-mingw/commit/c4c698ec8fd7413068fce2de966938b3f8462de8

--- a/Modules/makesetup
+++ b/Modules/makesetup
@@ -97,6 +97,9 @@
 	 	ExtraLibDir='$(LIBPL)'
 	 fi
 	 ExtraLibs="-L$ExtraLibDir -lpython\$(LDVERSION)";;
+Linux*)
+	 ExtraLibs='$(BLDLIBRARY)'
+	 ExtraLibDepends='$(LIBRARY_DEPS)';;
 esac
 
 # Main loop
@@ -285,7 +288,7 @@
 				BUILT_SHARED="$BUILT_SHARED $mod"
 				;;
 			esac
-			rule="$file: $objs"
+			rule="$file: $objs $ExtraLibDepends"
 			rule="$rule; \$(BLDSHARED) $objs $libs $ExtraLibs -o $file"
 			echo "$rule" >>$rulesf
 		done