Bill Kristol said Monday that Sen. John ThuneJohn ThuneSeven major players in Trump's trillion infrastructure push Trump’s great tech opportunity is in spectrum sharing Norquist warns GOP: Don’t link taxes, infrastructure MORE (R-S.D.) is reconsidering his decision not to run for president in 2012.

Kristol, the editor of The Weekly Standard and a major player in the GOP, said Thune is "rethinking a bit" about launching a White House bid.

Pressed on the matter by C-SPAN host Steve Scully on the network's "Washington Journal" program, Kristol responded, "That's what I've been told."

The Weekly Standard ran an extensive profile of Thune last fall. Thune subsequently announced he would not run for president in 2012.

A Thune spokesman says that the senator "remains focused on his work in the Senate."

Kristol said he does not expect the Republican presidential field to be set until this November. He later said his preferred ticket is Rep. Paul RyanPaul RyanPelosi: 'Of course' Dems can be against abortion Five fights for Trump’s first year Sunday shows preview: Trump stares down 100-day mark MORE (R-Wis.), with Sen. Marco RubioMarco RubioTop Trump officials push border wall as government shutdown looms Rubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs MORE (R-Fla.) as his running mate.

Ryan and Rubio have said they are not running for the White House.

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