Woods is seeking his 10th major triumph at this week's British Open, and Faldo fancies the 29-year-old American to repeat his win at St Andrews five years ago.
"I think Tiger is the favourite, obviously," the Briton told a news conference on Monday.
"He's played, he's won and he comes here with a mission, as always, and his record at every event where Nicklaus is basically handing over the torch, he's the one who wins every time."
Nicklaus is playing for the last time at St Andrews, where he won two of his three British Open titles, and Faldo thinks U.S. Masters champion Woods is on course to eclipse his compatriot's major record.
"You have to believe it, yes. Tiger has the desire," he said.
"We know that's one of his goals. He wants to be the greatest. So if he maintains that desire and the work ethic to do that, you have to believe that he could get there."
Faldo, who played a practice round with Nicklaus on Monday, has won six majors, including the 1990 British Open here.
"Obviously I love this place," the 47-year-old Englishman said. "It's very special, simple as that.
"It's steeped in history and words to describe it are probably not enough, most of the time."
Faldo says the tactics for winning around St Andrews remain the same, despite a number of alterations to the Old Course.
Woods did not hit a single bunker when he won the 2000 Open at the home of golf, and in two practice rounds has also avoided the sand.
"He's going to come and play to a game plan, simple as that," Faldo said. "But practice doesn't mean anything, practice is fun."
Faldo thinks there is a good chance of a first British winner since Paul Lawrie at Carnoustie in 1999.
"The guys have been performing well, so I think we've got plenty of players now," he said.
"I think in this kind of weather and the toughness, obviously Luke Donald has been playing pretty consistent, Lee Westwood is consistent in the wind, and there will be a few of us in the hunt, I'm sure."