Former New York Mayor Rudy Giuliani (search) is poised to endorse Arnold Schwarzenegger for governor in the Oct. 7 California recall election, the New York Post reported on Monday.

The Post reported that Giuliani, who had campaigned for 2002 gubernatorial candidate Bill Simon (search) and was expected to back him in the recall election, will likely throw his weight behind Schwarzenegger now that Simon has dropped out of the race to replace Democratic Gov. Gray Davis (search).

"Rudy will support him, and if it helps him [to campaign with Giuliani], I think we'll do it," a source close to Giuliani told the Post.

Schwarzenegger and Giuliani are both moderate Republicans, supporting abortion rights and some gun control. Giuliani's nationwide fame -- resulting from his noted leadership after the Sept. 11 terror attacks -- has made him one of the GOP's most valuable assets.

Simon dropped out of the race this weekend, saying that the crowded field would hurt Republican chances. Simon denied that he had been pressured by the Schwarzenegger campaign, though GOP congressional delegation chairman Rep. David Dreier (search) had been pushing Republican candidates to leave the field to make way for Schwarzenegger.

A Los Angeles Times poll released Sunday showed Republicans leading the California recall effort, but support split between three major Republicans. The division left Lt. Gov. Cruz Bustamante (search) leading with 35 percent support from those surveyed over Schwarzenegger, who received 22 percent backing.

State Sen. Tom McClintock (search) garnered 12 percent and former baseball commissioner Peter Ueberroth (searchearned 7 percent support in the survey.

The top three Republicans say Simon's withdrawal helps each of their candidacies. Ueberroth and McClintock have rejected calls to drop out of the race.

"If the most qualified candidate must defer every time a celebrity or a millionaire casts a longing eye on public office, we've lost something very important in our democracy, and it's called merit," McClintock said.

The GOP infighting is good news for Bustamante, who has been gathering endorsements and has even received grudging support from Davis.

Over the weekend, Davis called his lieutenant "the most qualified person on question number two," the first question being whether to recall Davis. 

The second question is who should replace Davis. Davis wouldn't reveal whether he would vote for Bustamante on the second part of the recall ballot, but said he would make his decision soon.

Meanwhile, Schwarzenegger is gathering more party support. With an already impressive campaign staff and list of supporters, Schwarzenegger has just added prominent GOP strategist Mike Murphy (search) to his team. Murphy led the presidential campaign for Sen. John McCain, R-Ariz.

Schwarzenegger also got a big boost on Friday when he picked up the endorsement of the Lincoln Club of Orange County (search), a powerful group of wealthy conservative Republicans.

The organization backed Simon in the last election, but this time around, phoned both Simon and McClintock asking them to quit.

Fox News' Claudia Cowan contributed to this report.