A number of names from Congress have been floated, including on Tuesday, Sen. Ted Cruz (R-TX):
Others think Cruz might be a possible choice for U.S. Supreme Court.
Cruz isn't the only Senator getting mentioned, as Sen. Jeff Sessions of Alabama has been rumored to be in line either for the job of Attorney General or Secretary of Defense.
There are also a number of lower profile Cabinet spots that need to be filled, and several members of Congress may be in the mix for those slots as well.
One report Tuesday said Rep. Tom Price (R-GA) was getting a look at being Health and Human Services Secretary.
When asked about that last week by my colleague Tamar Hallerman, Price laughed at the idea. But on Tuesday evening, he brushed by reporters in the Speaker's Lobby, as we tried to ask him about the job.
"No. Can't comment," Price said curtly, as he walked on to the House floor.
Other lawmakers being talked about for the Trump Cabinet include Rep. Jeff Miller (R-FL), the Chair of the House Veterans Committee, as some think he might be the new head of the VA.
"I haven't heard anything," Miller told me. "I'm just excited there's a potential to really reform the Department of Veterans Affairs."
Another name being floated is that of Rep. John Mica (R-FL), who lost his re-election bid last week - there has been talk that he might be a choice for Secretary of Transportation.
"I'm very honored that I'm even being considered," Mica told me. "It would be a great opportunity."
It's not clear when the President-Elect will start making his decisions. Mr. Trump takes the oath of office in just over two months.
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