Arnold Schwarzenegger (search) won't seek the California governor's office in conjunction with a recall election set for October, a source close to the actor told Fox News.

Schwarzenegger, 55, is said to have met Sunday with former Los Angeles Mayor Richard Riordan (search). Riordan and Schwarzenegger are close, and Riordan said last week that he would consider a run if Schwarzenegger decided against a bid.

"I would support Arnold Schwarzenegger in a second if he ran," Riordan said Friday. "I think he is sensational and if he doesn't run then I will have to make up my mind."

But Schwarzenegger consultant George Gorton told the Associated Press that Schwarzenegger hasn't made a decision yet, and is still considering the impact a run would have on his family.

"Arnold spent the weekend continuing his due diligence regarding a possible run. He has made no decision at this time. He will continue to weigh the pros and cons with his family and will continue to seek the counsel of supporters and colleagues," Gorton said.

Earlier this month, speaking to journalists in Berlin ahead of the European premiere of his latest film, Terminator 3: Rise of the Machines, the Austrian-born actor said his decision would depend on the political developments in his home state.

That was before a petition qualified to have a recall election on Democratic Gov. Gray Davis (search), who is facing approval ratings in the low 20s. 

California Secretary of State Kevin Shelley said last week that counties had reported 1.3 million valid petition signatures, well more than the 897,158 required for the recall to make it on the ballot. 

Lt. Gov. Cruz Bustamante ordered the election to be held on Oct. 7. Candidates have until Aug. 9 to declare their candidacies.

Schwarzenegger, who has eyed a political career on and off for years, has until recently insisted he was not thinking about running for governor.

He has, however, said he is capable of leading and putting things in order.