UPDATE 2:40 p.m.: The New York Daily News now has sources telling them that Giuliani will run for Senate.

The scenario is that Giuliani would run only for the last two years of Hillary Clinton's term and would use a win as a potential launching point for another run for president.

Giuliani's camp doesn't appear to have denied this, saying only: "Rudy has a history of making up his own mind and has no problem speaking it. ... When Mayor Giuliani makes a decision about serving in public office, he will inform New Yorkers on his own.

Original post below:

Rudy Giuliani won't run for governor in 2010, according to the New York Times.

Interestingly, the piece notes that there doesn't seem to be a final word on him running for Senate. He is not expected to challenge Sen. Kirsten Gillibrand (D-N.Y.), but some in the GOP establishment, like state party Chairman Ed Cox, have continued to urge him to do so.

Giuliani's camp maintains no decisions have been made.

From the Times:

Former Mayor Rudolph W. Giuliani has decided not to run for governor of New York next year after months of mulling a candidacy, according to people who have been told of the decision.

His decision is a blow to many Republican leaders, who had viewed Mr. Giuliani as the strongest potential candidate in a year in which voter anger and anti-Albany sentiment appear to be swelling.

Contenders from both parties have been waiting for months to hear what the former mayor would decide.

It was not clear what prompted the decision, but the prospect of potentially facing Attorney General Andrew M. Cuomo, who is quietly planning his own run for governor, may not have appealed to Mr. Giuliani, who suffered a bruising defeat in the 2008 Republican presidential primary. While many political analysts believe Mr. Giuliani would have comfortably beaten Gov. David A. Paterson, he would likely have faced an uphill battle against Mr. Cuomo, one of the most popular politicians in the state.

It remains unclear if the former mayor is considering any other political race in 2010. Some have urged him to take on the newly-installed Senator Kirsten E. Gillibrand, who has never run statewide and is still introducing herself to voters in parts of the state.

...

Maria Comella, a spokeswoman for Mr. Giuliani, said Wednesday that it was “premature” to say any decisions had been made, and cited the former mayor’s statements on television last weekend.