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.