WASHINGTON (AFP) - White House hopeful Barack Obama is close to picking a running mate, with Timothy Kaine, the one-term governor of the swing state of Virginia, a prime contender, reports said Tuesday. Kaine, 50, has told close associates that he has had "very serious" conversations with the Democratic senator about running as his vice-presidential nominee, the Washington Post reported. The Obama campaign has been combing through Kaine's background as part of an in-depth vetting, but is also taking a serious look at senators Evan Bayh of Indiana and Joseph Biden of Delaware, the newspaper said. Both Kaine and Obama were in Washington Tuesday but the Virginia governor denied they had any "secret meetings" planned. Asked if he was being vetted, Kaine told Washington radio station WTOP: "I have been on board with the campaign since February of 07 but I don't talk about my conversations with the campaign. "It's flattering to be mentioned. My mom loves it. But that's for the campaign to decide... and however they decide, they're going to make a very good decision as Senator Obama chooses his running mate," he said. One politician not considered as a leading runner for the VP slot is Senator Hillary Clinton, Obama's defeated rival for the Democratic nomination, both the Post and New York Times reported. Betting on the running mate stakes is intensifying in the run-up to the Democratic convention in late August. The relatively inexperienced Obama, 46, must take several factors into account, including a potential VP's pedigree as an office-holder and his or her experience in national security. Kaine, an early backer of Obama when much of the Democratic establishment was lining up behind Clinton, has only served as Virginia's chief executive since 2006. But the governor, a devout Roman Catholic, is a business-friendly moderate with appeal to working-class voters, and hails from a state that has not elected a Democratic presidential candidate since 1964. The Politico website Monday cited one source as saying that Kaine, who like Obama has roots in Kansas, "ranks very, very high on the shortlist" for VP nominee. Obama himself is staying coy about the selection process, but wants a running mate who shares his political outlook and will be a partner in government. "I'm not interested in a vice-president who I send off to go to funerals," the Illinois senator told NBC television on Sunday. "I want somebody who is going to roll up their sleeves and be willing to work." Obama reaffirmed that Hillary Clinton "would be on anybody's shortlist," but the newspaper reports said this appeared to be lip-service and that his campaign was confident that supporters of the former first lady would stay on-side even if she is not chosen. Unlike the tight-lipped Kaine, both Bayh and Biden have said they would serve as Obama's running mate if asked.