ABC News reported that Kaine is widely considered to be on Obama's possible list of vice presidential running mates.
After the meeting, Kaine was asked if Obama had asked him to be on the top of the ticket with him.
"I'm going to let the campaign speak for the campaign," Kaine said, as he has in the past. "He visited with my staff just to basically say hi to them and thank them for all their hard work," he added.
After their closed-door meeting, the two men attended an event together in Chester, Va. He praised Obama and criticized Republican presidential hopeful John McCain.
"One of the things that makes me laugh the most is people who say a vote for senator might be risky -- well, let me tell you what risk is," Kaine said to the group.
"When the economy is the front and center thing that all Americans are so concerned about right now, to put somebody in the White House that says 'I don't know much about economy,' that is risky folks. That's what Senator McCain said and that's risky," he added.
Notable deaths of 2014 [PHOTOS]