Former Sen. George Allen (R), who was unseated by Webb in 2006, has already announced he is running. Kaine, who has been weighing a run, is on vacation with his family until Monday, and according to a report in the Washington Post, will likely announce whether he is running as soon as next week. "I've urged him to run and I hope he will and I think he's in the final throes of a decision," Sen. Mark Warner (D-Va.) said Thursday of Kaine. "He's off on holiday with his wife." Stepping into an elevator, Warner declined to comment further. "That's all I'm saying." -- Dan Friedman and Dan Roem contributed to this post.