The annual chatter about which famous faces might show up on red carpets connected to this year’s Indianapolis 500 race and festivities has already begun.

Word is that Jake Gyllenhaal — who earned an Academy Award nomination for his portrayal of the confused Jack Twist in 2005’s “Brokeback Mountain” — could be in line for a prominent position.

Promoters of Disney’s “Prince of Persia: The Sands of Time” — in which Gyllenhaal stars — are said to be looking for a way to get the actor’s face front and center at the Indy 500 or “the race of all races,” as E! Online gossip columnist Ted Casablanca described it. The film opens Memorial Day weekend.

Gyllenhaal, however, won’t be waving the green flag or driving the pace car, according to officials at the Indianapolis Motor Speedway. They haven’t said who will perform those special duties, but an announcement about the 2010 pace car driver is expected soon.

There has been some contact between Gyllenhaal’s camp and the IMS, but nothing has been finalized, said Eric Powell, IMS public relations manager.

“We certainly welcome celebrities out for our event. How Mr. Gyllenhaal would fit in remains to be seen,” he said.

But there’s one more big role left to consider: grand marshal of the IPL 500 Festival Parade.

No word about who will fill that role has been announced, either, but folks at the 500 Festival seem eager to talk to Gyllenhaal’s people.

“We have a long list of celebrities we would like to be a part of our . . . parade. Jake Gyllenhaal is definitely one of those celebrities,” said Brandi Davis-Handi, spokeswoman for the 500 Festival. “While we have not been in contact with him directly, we would love to open the dialogue if he is indeed interested in coming to Indianapolis in May.”