ALBANY, N.Y. (AP) — Former New York City Mayor Rudy Giuliani, who many Republicans have been pushing to run for governor in 2010, is instead leaning more toward a run for U.S. Senate, according to two party advisers.

"From staff, we have been hearing that he has been indicating quietly and privately recently that governor might not be the best fit for him now," one adviser said Thursday. "But the U.S. Senate could be a perfect fit for him."

The adviser noted that nobody is saying Giuliani has decided, but it "certainly sounds" like he is less interested in running for governor. Another adviser echoed that.

The advisers spoke on the condition of anonymity because they weren't authorized to speak for the state Republican Party or Giuliani.

The New York Times, citing unidentified people told of the decision, reported Thursday that Giuliani, 65, wouldn't run for governor after months of considering it.

Giuliani spokeswoman Maria Comella disputed that report, saying he told her Thursday that he hadn't made a decision.

"When he comes to that decision he'll let everyone know," Comella said. Asked whether that meant Giuliani was still considering a run for governor, she said: "Correct."

Republicans have been watching polls showing that Giuliani, who came to be known as "America's mayor" when he saw grieving New Yorkers through the aftermath of the Sept. 11 attacks, would beat Democratic Sen. Kirsten Gillibrand in a hypothetical matchup in the Senate race next year. Gillibrand was appointed this year to fill Hillary Rodham Clinton's unexpired term when she became secretary of state.

Polls also show Giuliani trailing in a possible matchup with Democrat Andrew Cuomo, the popular state attorney general amassing a large campaign fund.

Cuomo hasn't announced a run for the office, once held by his father, Mario, but is widely expected to. He dropped out before a primary in the 2002 governor's race because he lacked support.

A Marist College poll this month found that Cuomo would beat Giuliani for governor, 53 percent to 43 percent. But Giuliani leads Gillibrand 54 percent to 40 percent in a possible Senate run.

"Clearly, running for the U.S. Senate is a far smarter move for him, particularly if has any national aspirations," Marist pollster Lee Miringoff said.

The poll surveyed 805 registered voters on Nov. 12, Monday and Tuesday. It has a margin of error of plus or minus 3.5 percentage points.

Former Rep. Sherwood Bohlert, a moderate New York Republican who served 24 years in Congress, called Giuliani "a leader of the party nationally, not just in New York," and said he thinks the former mayor would have an impact in Washington.

"Maybe another moderate in the Senate in Republican ranks would help bring the majority to their senses," Bohlert said.

Republicans in Albany were energized.

"I think, certainly, Rudy Giuliani would be a great U.S. senator and bring a unique perspective," said New York Assembly Republican leader Brian Kolb. He hasn't heard confirmation of the mayor's decision, but thinks Giuliani is leaning toward a Senate run.

"We should look at who is the best person for the job, first and foremost, and I think Rudy Giuliani is that guy," Kolb said.

Democratic Gov. David Paterson was skeptical of the reports when asked for comment Thursday. "If you don't mind I'd just rather wait for the mayor," he said.

Giuliani ran for Senate in 2000 in what was to be a titanic clash with Clinton. He withdrew when he found out he had cancer, which he has since beaten. He also withdrew from last year's presidential race, lacking support for the GOP nomination.

A third Republican adviser said Giuliani is expected to give Rick Lazio, the only announced Republican in the race, early notice of his decision. The adviser wasn't authorized to speak for the party and spoke on the condition of anonymity.

"We don't know what Rudy Giuliani is going to do," Lazio spokesman Barney Keller said. "We just know that Rick Lazio is running."

Earlier this year, some Republicans talked about Giuliani as "Rudy the Savior."

After losing the state Senate majority last fall after a half-century of rule, the GOP is shut out of every statewide office and the majorities of both houses of the Legislature for the first time in decades.

That locks the party out of critical control of patronage jobs and the power of incumbency to build electoral wins. Voter enrollment also is giving Democrats a nearly 2 to 1 advantage statewide, and growing.

Separately Thursday, Giuliani said that trying self-professed Sept. 11 mastermind Khalid Sheikh Mohammed in a federal civilian court in New York is unwise and unnecessary.

"There's no reason to put New York through this," said Giuliani, who was mayor when terrorists flew two hijacked planes into the World Trade Center and one struck the Pentagon. A fourth jet crashed in western Pennsylvania.

Meanwhile, the Democratic National Committee announced a new web video Wednesday that it says highlights Giuliani's "politically-motivated flip flop on whether suspected terrorists should stand trial in U.S. courts." It appears to show Giuliani praising the New York City trial of Sept. 11 conspirator Zacarias Moussaoui on Fox News' "Hannity & Colmes" program in 2006.

An e-mail requesting comment from Giuliani on the DNC video was not immediately answered.