.WASHINGTON (AP) – As speculation swirls, Barack Obama and John McCain are knuckling down to the work of choosing running mates with their nominating conventions just weeks away.

Current and former governors and senators seem the most serious contenders, though most of those mentioned are playing coy about any discussions with either campaign.

“I’m just not going to talk about my conversations with the campaign,” Democratic Gov. Tim Kaine of Virginia said Tuesday as he declined to confirm media reports that he has provided financial documents to Obama for review. Another, Republican Gov. Tim Pawlenty of Minnesota, said he has decided to stop answering questions about a spot on McCain’s ticket because of all the gossip.

Among others believed to be getting close looks: Indiana Sen. Evan Bayh, Delaware Sen. Joe Biden and Kansas Gov. Kathleen Sebelius for Obama as well as former Massachusetts Gov. Mitt Romney and former Ohio Rep. Rob Portman for McCain.

Several more have been mentioned as well. But it’s appearing less likely that Obama – a Democratic Illinois senator – will choose former rival Sen. Hillary Rodham Clinton of New York. And it’s still possible that McCain – a Republican Arizona senator – will choose former Pennsylvania Gov. Tom Ridge, whose support for abortion rights might upset conservatives whose enthusiasm McCain needs.