Luke Donald is ranked No. 1 in the world despite never having won a major championship. (Chris O'Meara/AP)

When Luke Donald stuck his tee in the ground just after 8 a.m. Thursday — and the blazer-wearing announcer at Muirfield Village Golf Club introduced him to the assembled crowd, simply, as hailing from Hemel Hempstead, England — a notion crept into the back of Donald’s brain, whether he wanted it there or not. It went roughly like this: “For the first time, I’m playing a tournament as the number one player in the world.”

“Just a sneaking little thought,” Donald said. “It felt good.”

The last time the U.S. Open was held at Bethesda’s Congressional Country Club, back in 1997, Tiger Woods was coming off his first major championship at the Masters, and was ranked No. 1. In the week prior to the 13 Opens since, Woods has been No. 1 all but once. The exception came in 1999, played in Pinehurst, N.C., when David Duval briefly surpassed Woods.

But with the Open starting two weeks from Thursday, Donald — owner of no major championships, winner of seven tournaments worldwide in a career that spans more than a decade — is likely to be the top-ranked player in the world. His opening round of 2-under-par 70 Thursday at the Memorial Tournament included a sloppy first nine that belied his current standing as the game’s most consistent force. But he made four straight birdies on the back to pull within four shots of leaders Chris Riley and Rory McIlroy, who opened with 66s.

The signs that things have changed for Donald in the past six months — when he climbed up the rankings with a victory at the Accenture Match Play Championship, then vaulted to No. 1 by beating then-No. 1 Lee Westwood in a playoff at last week’s BMW PGA Championship on the European Tour — were all over Muirfield. He was paired with four-time major winner Phil Mickelson and current Masters champ Charl Schwartzel, the marquee group. He heard a few shouts of “Number one!”, off which he fed.

“As a kid, you dream about winning majors and winning tournaments,” Donald said. “But for me, I always kept an eye out on the world rankings and had an interest in it, but I suppose for the bulk of my career, Tiger was so far ahead that it never really crept into my mind.”

Woods’s fall from the top of the rankings — his uninterrupted hold of more than five years ended last October — is just one indication of how his previous vice-like grip on the game has completely loosened.

He isn’t here for the Memorial, an event he has won four times; he’s home in Florida rehabilitating his ailing left knee and Achilles’ tendon. He has fallen to 13th in the world rankings, lower than at any time since he won his first major. And even Sean Foley, his swing coach since last August, can’t predict the shape he’ll be in when he arrives at Congressional — assuming he does.

“I don’t know,” Foley said earlier in the week. “I talk to him every day, and I have no idea.”

So, meanwhile, the accolades — tournament victories, the top spot in the rankings — are left for others. And an examination of Donald’s game and his results show why he has stepped through that opening. He doesn’t bomb his drives; his average of 277.7 yards coming into this week ranked 163rd on the PGA Tour.

However, he makes up for it with an excellent short game and smart thinking.

“He’s going to win a lot more here in the near future, and the reason being is because he knows his game,” said Fred Couples, who played with Donald during the first two days of this year’s Masters. “. . . He makes very few mistakes.”

Which is why, when he hit a poor shot Thursday from a greenside bunker at No. 9, then flubbed the ensuing chip and made double bogey, the gallery murmured. Donald’s results this season are staggering. He missed the cut in his first event of the year, and has played 11 times since. The results: two wins, two seconds, two ties for fourth — at the Masters and the Players Championship — and precisely no finishes outside the top 10.

The next step, then, would be a major. Donald has contended a few times, battling with Woods at the 2006 PGA Championship before a final-round 74 left him third, flirting with the lead at this year’s Masters before Schwartzel closed with four straight birdies. Could it come at Congressional?

“I’ve always said if you’re playing well, you can win any tournament,” Donald said. “It doesn’t really matter the circumstances. I’m obviously on a big high, confidence-wise.”

Because when he tees it up there, he’ll likely be in his third week as the No. 1 player on the planet.