Sen. Tim Kaine Timothy (Tim) Michael KaineBarrett seen as a front-runner for Trump Supreme Court pick Biden promises Democratic senators help in battleground states Second GOP senator to quarantine after exposure to coronavirus MORE (D-Va.) says he doesn't think presumptive Democratic presidential nominee Hillary Clinton Hillary Diane Rodham ClintonJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Momentum growing among Republicans for Supreme Court vote before Election Day Warning signs flash for Lindsey Graham in South Carolina MORE is going to ask him to be her running mate, but he won't rule out accepting the offer if she asks.

Kaine, who is high on media speculation lists as Clinton's vice presidential pick, told C-SPAN he loves being mentioned in VP discussions, but his "gut" tells him he won't get picked.

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"I was vetted for this spot back in '08, and I love being mentioned but my gut was never saying 'I think it's going to be me,' and I don't feel that differently now," Kaine said, in a preview clip given to The Hill.

The full C-SPAN American Profiles interview with Kaine will air on Sunday night.

Kaine paused and chose his words carefully when asked what he would say if Clinton told him she needed him on her ticket.

"Well, look. I really like my job and I want to stay," Kaine said.

"I think I can help her win, and I think I can help her win most by helping her win Virginia, and that's what I am doing already.

"So, she's got a lot of directions that she can go, and look, she's going to choose a person who is the best suited to help her govern and to help her win."

Kaine said he plans to stick around a long time in the Senate.

"I really love my committees and so ... I will be up for reelection in 2018, and I'm kind of taking John Warner as my role model.

"He was in the Senate for 30 years and did a great job for Virginia and was courageous," Kaine said, referring to the state's longtime Republican senator.

"I hope to be here for a long time. ... I've got a good platform right now. I really like my job.

"I'm a happy senator, and I'm not looking for another one."