SOUTHAMPTON, N.Y. — Rickie Fowler knows he can win major championships. He says everyone in golf knows that. So how about this week in the U.S. Open?

Majors have not been kind to Fowler, who either gets teased or slammed by them. In April, he came up one shot short of Patrick Reed at the Masters. Fowler also was the runner-up at the U.S. Open and British Open in 2014. In all, he has eight top-five finishes in Grand Slam events. He also has missed cuts in seven majors.

So he was asked again Wednesday: How about this week?

‘‘Yeah, definitely, I’ve been very close,’’ Fowler said. ‘‘I feel like there’s a few you could look at and say, ‘If it wasn’t for that one guy, we would have won.’ There was a couple of majors where there was a runaway or someone just happened to play just that little bit better. There’s some scores that I’ve shot that have been good enough to win majors, but we haven’t been able to get it done that specific week.

‘‘I kind of like to look at it as I’m good enough, and I basically won a major. I won the Players [in 2015] against, arguably, the best field we play all year on a golf course that is a very good test, as well. No, we’ve just got to happen to get one done at the right time and have that week.’’

Shinnecock Hills would be a good place for it to happen. Fowler rates it as one of his favorite American courses, one he has played more often than any heading into a major on that layout. He has been on Long Island for more than a week, with practice rounds at Shinnecock and several other highly rated courses.

Fowler even played with Patriots star Tom Brady on Tuesday at Friar’s Head, another revered course on the island.

‘‘I’ll tell you what, Tom Brady can putt,’’ Fowler said. ‘‘If I can take that into this week, that’s one thing I can take from him that can help me.’’

Fowler can do everything with a golf ball, and he has been considered the best player not to win a major since Sergio Garcia captured the 2017 Masters. At 29, he should be in his prime competitive years, and he hardly lacks experience. This will be his 10th U.S. Open.

Among Fowler’s victories are that Players Championship in 2015 and the Deutsche Bank in the FedEx Cup playoffs the same year.

Also, as a member of three Ryder Cup and two Presidents Cup teams, Fowler shouldn’t be bothered by pressure in the big events.

Yet there are no major trophies in his collection.

‘‘We all know I’m good enough to win; I know I’m good enough to win,’’ he said. ‘‘Being prepared and making it happen that specific week, there’s been a few guys that have been very good at that: Jack [Nicklaus], Tiger [Woods]. Phil [Mickelson] didn’t get his first for a while, so there’s still hope. I’m not too worried about it.’’

Nor is Rory McIlroy, who by the age of 25 owned four major titles. One of those was in the 2014 British Open, where he beat Fowler by two strokes. At the PGA Championship a month later, McIlroy won again and Fowler finished third.

While McIlroy would prefer to see his own name engraved on those trophies, he’s certain Fowler will win his share of majors.

‘‘I’d be very surprised if Rickie didn’t have multiple majors by the end of his career,’’ McIlroy said. ‘‘He’s a great player. Again, he’s played great in majors. He could have won a couple in ’14, and I was the one that got the better of him there.

‘‘But he’s put himself in positions. . . . The more times Rickie puts himself in a position, the better his chances are of winning one. But I think everyone in this room would be really surprised if he wasn’t to go on and win at least more than one major in his career.’’