ST. ANDREWS, Scotland — Rory McIlroy is bullish on the GOAT.

McIlroy believes Tiger Woods has a chance to win his 16th career major championship and fourth British Open title this week. If Woods were to win another Claret Jug, he would become the first player to ever win three at St. Andrews, which he calls his favorite course in the world.

“I think the way the golf course is and the way the conditions are, I could certainly see it,’’ McIlroy said. “It’s going to be a game of chess this week, and no one’s been better at playing that sort of chess game on a golf course than Tiger over the last 20 years.’’

McIlroy played alongside Woods on Monday in the Celebration of Champions four-hole exhibition featuring past Open champions. Woods birdied two of the four holes, Nos. 2 and 18, on which he drove the green.

“For those four holes, he was moving better than I’d seen him move in a while,’’ McIlroy said, referring to Woods’ surgically repaired right leg, which nearly had to be amputated after his one-car crash in February of 2021. “And his swing … hitting the golf ball and swinging the club aren’t the issue. It’s the walking part of it that’s the struggle. But he seemed to be moving well. Everything looked pretty good [Monday], so that’s encouraging.”

Woods played all four rounds at the Masters in April and withdrew after the third round of the PGA Championship in May because his leg was in distress. He said he’s stronger than he was at those two tournaments.

Woods, too, said he has been targeting this Open since the moment he realized he’d be able to play tournament golf again. After he finished the Masters, Woods said he was definitely going to play St. Andrews, but wasn’t sure about the U.S. Open or PGA.

“Once I realized that I could possibly play at a high level, my focus was to get back here at St. Andrews to play in this championship,’’ Woods said. “Being it’s the most historic one we’ve ever had, I just didn’t want to miss this Open here at the home of golf. This has meant so much to me.’’

It’s the place where he made his Open debut as an amateur in 1995, the place where he won his first of three Claret Jugs in 2000 and the place where he completed his career Grand Slam in 2005.

Including that four-hole exhibition on Monday, Woods has played 58 holes of practice this week on the Old Course. He practiced at the range on Wednesday, but didn’t play any holes.

Woods has had the look of someone soaking it all in this week, posing for numerous pictures on the Swilcan Bridge. He posed with Lee Trevino, Jack Nicklaus and McIlroy on Monday. Tuesday, he posed with his girlfriend, Erica.

“I have a photo in my office when I first played my first practice round, me sitting there [on the bridge], and it means a lot,’’ Woods said. “I mean, the history and the people that have walked over that bridge. To Lee and Rory and Jack, and just stand there with them, that’s history right there. Everyone has seemed to have made their farewell there.’’

Asked if he’ll feel any differently when he walks over the bridge for the final time this week in competition, knowing the Open may not be back at St. Andrews for another five, six or even seven years, Woods said: “I don’t know, if it is that long, whether I will be able to physically compete at this level by then. It’s also one of the reasons why I wanted to play in this championship. I don’t know what my career is going to be like.

“I don’t know how many Open Championships I have left here at St. Andrews, but I wanted this one. It started here for me in ’95, and if it ends here in ’22, it does. If it doesn’t, it doesn’t. If I get the chance to play one more, it would be great, but there’s no guarantee.’’