Rudy Giuliani says he is ending his bid for GOP presidential nomination, endorsing Sen. John McCain.

MIAMI, Florida (CNN) -- Former New York Mayor Rudy Giuliani ended his GOP presidential race and endorsed rival Sen. John McCain of Arizona on Wednesday.

And sources say California Gov. Arnold Schwarzenegger might endorse McCain on Thursday.

"This is a man who is prepared to be president," Giuliani said of his "old friend."

Giuliani said McCain gives the Republican Party the best chance to hold onto the presidency.

"I am very proud to endorse my friend and fellow Republican -- a hero -- John McCain," Giuliani said at the Ronald Reagan Presidential Library in Simi Valley California, two hours before the Republican presidential candidates were to face each other in their final debate before the Super Tuesday contests next week.

Meanwhile, two Republican sources told CNN that California Gov. Arnold Schwarzenegger is in discussions about endorsing McCain.

One of the sources said, "you can safely describe the conversations as progressing and productive." The second source described the endorsement as "more than expected" and said the conversations were aimed at arranging a Thursday announcement.

Giuliani described McCain as "the other best candidate."

"I made it clear before I had to make this decision [to drop out] that had I not run, I'd be supporting John McCain," Giuliani told reporters on a flight to Burbank, California, for the debate.

The debate is being sponsored by CNN, the Los Angeles Times and Politico, and begins at 8 p.m. ET.