ABC News’ Tahman Bradley, Teddy Davis and Ayana Harry report: Virginia Governor Tim Kaine downplayed speculation Tuesday that he is on Sen. Barack Obama’s list of potential vice-presidential candidates. "I haven’t sought it, I’m not running for it, I’m not asking for it," Kaine told a crowd of reporters in Washington, DC who waited for him to finish an interview with WTOP radio. Rumors about whether Obama will choose the Virginia governor as his running mate swelled Tuesday after the Washington Post reported Kaine told unspecified "close associates" that he has had "very serious" conversations with Obama about joining him on the 2008 Democratic ticket. He has also provided documents to the campaign as they check his background, the Washington Post reported Tuesday. ABC’s Jan Crawford Greenburg has also put Kaine on Obama’s "very short list." After his interview with WTOP, Kaine was greeted by a swarm of reporters asking whether he told friends that he’s talking with Obama about being a vice-presidential candidate. "My conversations with the campaign stay with the campaign," Kaine said, adding that he did not meet with Obama today and is not planning to do so. Obama is in Washington DC Tuesday for meetings. However Kaine joked that news reports that he is on Obama’s list of candidates are making his mother happy. "My mom loves seeing me on the lists, that’s fun for her," he said. Reporters have begun to track the movement of potential vice-presidential picks carefully. During Kaine’s interview with WTOP Radio in Washington, D.C., he indicated that he has a private event planned with his daughter later Tuesday. A Kaine aide tells ABC News that the Obama vice-presidential prospect is headed to Chincoteague Island, Va., on Tuesday in order to be there for Wednesday’s annual Chincoteague Pony Swim with daughter Annella. The pony swim is expected to take place on Wednesday between 7:00 am – 9:00 am ET. With Kaine slated to spend the rest of Tuesday and most of Wednesday on the island, speculation is swirling as to whether he will be engaged in any VP-related talks or briefings. On Thursday, Kaine is scheduled to be back in Richmond for a 9:00 am ET radio interview with WRVA in Richmond, Va.