Arnold Schwarzenegger: I Won't Say if My Son Should Run ... But John Kasich Will

John Kasich was true to his word Friday, trying to insert himself in interviews ... even with the likes of Arnold Schwarzenegger.

Arnold showed up at the Montage hotel in Bev Hills for a Kasich fundraiser, when our photog asked if his super good-looking son Patrick would ever run for a political office ... after all, he's a Kennedy.

Arnold was guarded, and that's when Johnny jumped in with his 2 cents, which honestly made it a little entertaining.