Apparently Kaine hasn't actually said NO, (yet)...

The Virginian Pilot has issued a correction on former Governor and current DNC Chair, Tim Kaine, regarding his interest in running for Virginia's open U.S. Senate seat. 

According to the Virginian Pilot, "Kaine previously said that he wasn't interested in the office if Webb didn't seek re-election." 

So, the real question is will Kaine run?  The Virginian Pilot does a good job, for the most part.  Maybe and actual quote from the source would be good next time. 

Tim Kaine not interested in open U.S. Senate seat

According to a story on the Virginian Pilot's website, former Governor and current Democratic National Committee Chairman, Tim Kaine, has indicated that he is not interested in running for the now open U.S. Senate seat in Virginia.  Perceived by many on the left to be the strongest candidate to run against either of the declared GOP candidates, Kaine's announcement will keep the speculation going as to who will run for the Democrats in a seat that is now considered by several to be a possible to likely GOP pick-up. 

So far there have only been two announced GOP candidates, the GOP establishment favorite former Governor and U.S. Senator, George Allen (who Jim Webb defeated in 2006), and Tea Party activist Jamie Radtke.  Whoever emerges for the Democrats will face a political landscape that is currently not favorable for them. 

Some other names that have been mentioned are former 5th District Congressman Tom Perriello, former 9th District Congressman Rick Boucher, former DNC Chair and Democratic Candidate for Governor in 2009 Terry McAulliffe, State Senator "Chap" Petersen, and so on and so forth...