Within his inner circle, there is still considerable debate as to whether the job represents a good fit for the former GOP presidential candidate or even whether Giuliani is serious about seeking the seat currently held by embattled Democrat David Paterson.

In a meeting earlier this month with Guy Molinari, the former congressman and Staten Island Borough president, Giuliani wondered aloud if his style could produce results in New York’s notoriously dysfunctional state capital.

“He expressed concern about how effective he would be,” recalled Molinari, a longtime Giuliani associate. “One thing I’ve learned about Rudy is that he wants to be effective.”

“The question is whether he could do well in a Democratic-controlled Assembly,” Molinari added. “The landscape in Albany is different.”

Several Giuliani insiders, who asked not to be named in order to speak freely, harbored serious doubts that the former two-term mayor would run for the governorship in 2010. According to his associates, Giuliani will not announce his plans until after the New York City mayoral race in November.

“I think there is, at best, a 20 percent chance that he runs,” said one Giuliani insider. “He just wants to get on with his life. He wants to be relevant; he wants to have a say. But he doesn’t want to run for governor.”

“I don’t think he’s running; he’s not doing the things you need to do to run,” said an old Giuliani friend who keeps in touch with the former mayor. “He’s not saying no, but he’s not fundraising.”

This week, however, by wading into the contested race for state Republican Party chairman, Giuliani sparked talk that he was laying the groundwork for a statewide run.

After encouraging state Chairman Joe Mondello to step aside, Giuliani political hands began making calls this week to gauge support for Giuliani ally Henry Wojtaszek, a Niagara County GOP chairman who is pursuing the position against Giuliani foe Edward F. Cox, a New York City attorney who backed John McCain in the 2008 GOP presidential primary.

One Giuliani associate agreed that the former mayor’s decision to get into the weeds of state party politics — something Giuliani hasn’t been known to do in the past — is a sure sign that he is thinking about a race.

“He’s focused; he’s watching it,” the longtime Giuliani insider said Monday. “This is clearly an uptick in interest.”

In late July, Giuliani raised eyebrows when he told an audience at a Crain’s New York breakfast, “If I thought I could make a real difference in the state, really change things ... then I would [run].”

“I got elected mayor, I believe, on the theory of: It can’t get worse,” Giuliani said. “So if it gets to that point, maybe I’ll decide [to run].”

Giuliani has further fueled speculation about a possible run by traveling through New York in the past few months to discuss a prospective bid with party officials. Last month, Giuliani huddled with county chairmen after he delivered a “Get Motivated” speech in Albany.

Rep. Peter King (R-N.Y.), who is close to Giuliani, said the former mayor brought up the prospect of a gubernatorial bid during a lunch at the Capitol Hill Club last month.

“I was surprised by how focused he seemed. He had given it a lot of thought,” said King, noting that Giuliani seemed far less interested in a gubernatorial campaign when the former mayor brought it up in a conversation late last year. “He equates the challenges New York faces right now to the challenges he faced in New York City in 1993.”

“He’s not definite, but he’s leaning in that direction,” King said, estimating the chances of Giuliani running at better than 50 percent. “He’d like to be governor.”

Giuliani insiders say they are confident Giuliani would have the support of the party establishment if he decided to run. Erie County Executive Chris Collins and former Rep. Rick Lazio are also mentioned as potential GOP candidates.

“Broadly speaking, there are a lot of party chairs out who have encouraged him to run,” one Giuliani aide said Monday.

A Siena College poll released Monday showed Giuliani trouncing Paterson 56 percent to 33 percent in a prospective contest. But the poll found Giuliani trailing Democratic Attorney General Andrew Cuomo 53 percent to 40 percent.

Skeptics have been quick to point out that Giuliani might be attempting to gin up attention in order to raise badly needed political funds. Through the end of June, Giuliani had nearly $3 million in campaign debt left over from his presidential bid. Giuliani’s political action committee, Solutions America, reported just over $1,000 on hand this month.

In the weeks ahead, Giuliani is planning to hit the campaign trail on behalf of Republican gubernatorial candidates in Texas, New Jersey, Florida and Virginia.

Hank Sheinkopf, a veteran New York City-based Democratic strategist, suggested that with his visible maneuvering this week Giuliani was simply trying to push Cuomo, widely seen as the candidate to beat should he challenge Paterson in a primary, into showing his cards.

“Rudy Giuliani is running for governor when he raises the $40 million needed to run for governor,” said Sheinkopf.