DUBLIN, Ohio — Phil Mickelson has won 40 tournaments around the world, including four major championships. He's won events honoring Arnold Palmer, Byron Nelson and Ben Hogan.

But he's never been handed a trophy on a Sunday by Jack Nicklaus.

He hopes to correct that this starting today at the Memorial Tournament.

As Mickelson was coming up Muirfield Village's 18th fairway in a charity skins game on Wednesday, he and the Memorial's founder and host had a little chat.

"He said he'd dearly love to win my tournament and I said, 'Well, Phil, I'd dearly love to have you win it,"' Nicklaus said. "I sort of gave him the line that Bobby Jones said about St. Andrew's, that no golfer's resume as a champion is complete unless they win at St. Andrew's. So I told him, 'No golfer's resume would be complete unless (they) win at Muirfield."

Mickelson may never be in a better position to do it. He is still riding the crest of his emotional win at Augusta National and could bypass Tiger Woods to become the No. 1 player in the world.

Woods is making his return to competition after sitting out three weeks due to a neck injury. After a winter of rumor and innuendo in the wake of his admission of marital indiscretions, Woods has played sparingly and at times poorly. His swing coach, Hank Haney, and he went different directions recently, too.

But that doesn't mean Woods is ready to step aside. Or that he's focusing only on the threat of one player.

"There's so many guys," said Woods, who has won the Memorial a record four times. "If we're playing match play or we're playing matches one on one, say, like (Roger) Federer and (Rafael) Nadal do, that's a totally different deal. We may be at the same event, but we may not all be in contention at the same time. When we are, we go at it."

Nicklaus played with Mickelson Wednesday and watched him shoot a 6-under 30 on the difficult back side at Muirfield Village.

"I've seen him play nine holes," said Nicklaus. "Those nine holes he looked like he should be a layup No. 1. You don't shoot 30 every time you play, though. He just drove it a mile, his irons were great. He played very well."

But Mickelson has played well only in spurts so far this year. In addition to the victory at Augusta National, he finished second to fast-rising Rory McIlroy at Quail Hollow.