Kaine made his comments Saturday in front of a crowd of nearly 1,500 party members at the state party's annual Jefferson-Jackson fundraising dinner in Richmond, The Hill reported. Sen. Jim Webb, D-Va., is retiring.
Kaine met with President Obama this past week to discuss the Senate race, but he didn't say if the president asked him to run.
"I have a job that I absolutely love," Kaine said. "I get to travel this country on behalf of the president, advocating for the values I believe in … . I was completely focused on doing that all the way through 2012."
Democrats think Kaine is the best chance to hold onto Webb's Senate seat next year. Former Sen. George Allen is running on the Republican side.
If Kaine decides not to run, former Rep. Tom Perriello, D-Va., would likely be the Democrats' choice, The Hill said. He was defeated in a re-election bid in November.
Perriello was in attendance at the fundraiser and said, "I certainly hope Tim Kaine runs."
Perriello said if Kaine decides not to run, he would "seriously consider" running.
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