"Probably the leading contender among the outsiders is a US Republican Representative from Oklahoma, Jim Bridenstine, who since being elected to Congress has quickly become a darling of the commercial space industry. ... Not only does [Scott] Pace presently work at a university in the nation's capital, he has also served George W. Bush on space policy and was 2012 Republican nominee Mitt Romney's chief space adviser."
Keith's note: FWIW the rumors here in DC suggest that Mike Griffin is looking for a position in the defense sphere. Mark Albrecht says that he's not interested in going back to government, Bob Walker notes that his lobbyist stance makes him (probably) ineligible, and Eileen Collins annoyed the Trump people when she suddenly backed out of the endorsement that they thought they were going to get.
If I were betting on horses it would be Bridenstine and Pace. Pace worked at NASA Headquarters for a number of years and has experience in the running of a large government agency with tens of thousands of employees and a multi-billion dollar budget. Bridenstine ran a small air & space museum and now has Potomac Fever and wants to stay in Washington when his self-imposed term limit expires. Pace is measured and deliberate with a deep understanding of space policy whereas Bridenstine is all fired up and motivated to enable change in the way that we explore and utilize space. It would be nice (for once) for a President to pick someone to run NASA with actual experience in running big things. It would also be nice to have an energetic advocate for space promoting NASA's efforts to a broadening audience.
Alas, as that song at Trump rallies often reminded us "you can't always get what you want". Stay tuned.