Sen. John McCain (R-Ariz.), incoming chairman of the Senate Armed Services Committee, said Monday that White House Chief of Staff Denis McDonough had contacted him about his thoughts on who should be the next defense secretary.

“I said Lieberman,” McCain told our colleague Steven Ginsberg as he got off the Amtrak Acela from Washington to New York. McCain laughed and said McDonough thanked him for his input, but that McCain did not think his close pal, the former senator from Connecticut, a Democrat turned Independent, would be considered for the job. (After all, he did endorse McCain over Obama in ’08.)

McCain also said he did not think Department of Homeland Security Secretary Jeh Johnson would be considered for the job.

“Interesting times. Interesting times,” he said, before heading out of Penn Station for an appearance on the Colbert Report and then back to Washington Monday night.

Loop Fans may recall that Sen. Ted Cruz (R-Tex.) last week promoted Lieberman as “one strong option” to replace outgoing Defense Secretary Chuck Hagel. “I urge the President to give him full and fair consideration for this critical position,” Cruz said in a press release.  And we predicted the suggestion would excite McCain.

The drumbeat is picking up.