Brooks Koepka is calm and cool as he leads the PGA Championship

 ST. LOUIS — Even when he is preparing for the next-to-last round in a major championship, Brooks Koepka makes sure he goes out in the morning to lift weights. And even in the public gym, he says, people overlook him.

 It happened again on Saturday when he went with his usual workout partner, Dustin Johnson. “Everybody wanted a picture with Dustin,” said Koepka, the two-time U.S. Open champion. “They were talking about him as we left and I was just standing there laughing. They were like, `Did you see that No. 1 player in the world was here?’ ”

Koepka just laughed at that. By Saturday night, Koepka — boosted by the kind of dismissal that gets him pumped up — was the No. 1 player in the PGA Championship. He shot 4-under-par 66 to finish the third round at 12 under, two strokes ahead of Adam Scott. Koepka said he plans to be back at the same gym Sunday morning and has all the confidence that he will still have enough strength to lift the Wanamaker Trophy Sunday night.

He nearly started running away with the tournament, holding a five-stroke lead before he bogeyed the 14th and 15th holes. Still, he did better than many other players who wobbled on an eventful day at Bellerive Country Club. Should he hold onto the first 54-hole lead of his career, Koepka will be the first to have won the U.S. Open and PGA in the same year since Tiger Woods — one of those close behind Koepka on an all-star leaderboard.

 “With so many big names, you would expect two or three of them to really make a push to get off to a good start and challenge me, I guess,” Koepka said. “Yeah, there’s a lot of star power and there should be. It’s a major championship. You should see the best players in the world come to the top.”

Woods finished his second-round 66 in the morning then shot another one to finish at 8 under, tied for sixth, one shot behind Jon Rahm, Rickie Fowler and first- and second-round leader Gary Woodland. The latter dropped four strokes with a bogey and triple bogey on 9 and 10. Johnson needed three birdies on his final four holes to shoot 72 and stay within seven shots. Jordan Spieth (4 under) took himself out of contention with a 7 on the par-4 12th.

 Koepka kept churning, making the turn in 30 and refusing to be derailed by some loose swings on the back nine. Saving bogey was not easy on 15 after his drive landed right behind a tree. “It was impressive that it ended up there. You would think it would have hit somebody’s foot and kind of gone to the side,” he said.

 He rallied with a 10-foot par save on the par-3 16th and made birdie on the par-5 17th.

Scott birdied both 16 and 17 and put himself into good position for his second major title, after the 2013 Masters. “It has been quite a while since I was really in contention, which has been quite frustrating. I’m glad I got a dose of it today because I want a whole lot tomorrow,” he said.

 It has been an emotional week for Scott and his fellow Australians (Jason Day is at 8 under) after the death of countryman and fellow tour pro Jarrod Lyle. “I don’t even really know if we have all really had time to reflect on it and let it sink in,” Scott said. “But I think that a part of everyone is playing for Jarrod out here this week.”

 Koepka is expecting a great show, given the protagonists. “These are names that I’ve grown up watching, that everybody else loves to watch play,” he said.

  He is well aware that some people do not yet consider him a big name. Koepka said that he was fueled during the Open at Shinnecock Hills by the sight of his name having been omitted on a televised list of “Notables Scores.”

  That sort of thing motivates him, he said, adding that he does consider himself a Notable: “You can’t hide when you’re on the top of the leaderboard. You can’t hide my name.”