06/26/2012 03:51 pm ET Updated Jun 26, 2012

John Thune On Being Mitt Romney's VP: 'I Don't Think You Ever Close The Doors Entirely'

WASHINGTON -- Sen. John Thune (R-S.D.) on Tuesday ducked questions about whether he has been talking to Mitt Romney about being the candidate's vice president, though he did not rule out the possibility of taking the job if it were offered to him.

"I don't think you ever close the doors entirely, if you're interested in public life and making a difference," Thune told reporters, when asked if he's interested in the slot. "But ... I'm not seeking it, I'm not pursuing it, and I like the job I have."

He declined to say if he has submitted materials to Romney's camp for being vetted.

"I'm not talking about the process," Thune said. "It's ultimately a decision that they have to make. They'll make a good one, I'm confident of that."

Thune, who is chairman of the Senate Republican Policy Committee, is one of a handful of lawmakers whose names have been floated as a possible running mate for Romney. Sens. Marco Rubio (R-Fla.) and Rob Portman (R-Ohio) are on Romney's list, as is Rep. Paul Ryan (R-Wis.).

Thune said he's "a big fan" of the people on Romney's list and that there's no need to rush the process. Still, he said again that he's open to being considered.

"I've just said you don't rule anything out," Thune said.

Senate Minority Leader Mitch McConnell (R-Ky.) laughed when Thune got the question -- and avoided answering it -- at a GOP leadership press conference earlier in the day. McConnell said he is not in talks with Romney's campaign about whom he supports.

"I haven't had any discussions," McConnell told reporters. "We're anxiously awaiting their decision just like you are."

Below, a list of some potential candidates who've said they're not interested in serving as Romney's vice president:

Veepstakes 2012