Sen. Sherrod Brown (D-OH) testifies on Capitol Hill on March 30, 2011, in Washington. | Getty Sherrod Brown throws cold water on Clinton VP talk

Ohio Sen. Sherrod Brown may support Hillary Clinton, but the Democratic senator provided one reason Tuesday that he might think twice before accepting an invitation to be her running mate: Ohio Gov. John Kasich would nominate his replacement if the ticket is successful.

Chris Matthews opened his interview with Brown on MSNBC's "Hardball" by asking whether his name was being considered by Clinton's campaign.


"Tim Kaine and I were talking together today at lunch. We've very good friends and his name and my name are mentioned," Brown said, referring to his colleague from Virginia who has similarly deflected questions about joining Clinton's ticket. "We have no idea how this is done."

"I've not been asked by Hillary's campaign to talk about this. I know they're looking at people, but my interest all along has been staying in the Senate and fighting for the issues that you talk about on your show," Brown said, talking up his agenda for working-class families.

If he were on a winning ticket with Clinton, Brown noted, Ohio's Republican governor would appoint his replacement. "And that bothers me," he said.

"So I have no idea what she's going to do. I know that my focus is doing this job and come August and September, besides my Senate duties, is to fight for Hillary Clinton to be the next president," he said.

Brown, whose wife Connie Schultz is a journalist, gave a similar response to CNN's Jake Tapper on Sunday.

"We know you have to ask that question. I'm not going to answer it any differently. I respect the work you do. I'm not going to answer any differently," Brown said. "I love the job I'm doing."