From the December 20th edition of Fox News' The Five:
BRET BAIER: There are obviously names that are floated around in Washington. It had been rumored that -- which is why I asked the question, out at the Reagan Defense Forum, that he was considering it, and that possibly he might leave. I agree with you that it's -- it's going to be tough to fill.
The other thing to point out is that the president came out at the Army-Navy game and made the early announcement that he was going to replace the Chairman of the Joint Chiefs, General Dunford with Army General Milley, also very well respected in all kinds of circles, but announcing that early, so, that transition's happening as well next year.
I think, you know, he has -- President Trump has talked to Jack Keane a lot. He has talked to a number of other people who, on Capitol Hill are possible. Lindsey Graham has expressed privately that he would love to be Defense Secretary.