Rory McIlroy believes he can challenge for the U.S. Open title on Sunday, saying a third-round 68 has given him "a pretty good shot".

The Northern Irishman began on Thursday with a three-under 67 but turned his numbers around in the second round when a 76 looked to have scuppered his hopes.

On Saturday, moving day at Winged Foot, McIlroy had three birdies and just one dropped shot in the kind of solid performance he would sign for again in the final round.

Four-time major winner McIlroy, who was 22 years old when he won the 2011 U.S. Open, was back on the leaderboard.

On a course where American Matthew Wolff, just 21, was setting the pace, McIlroy was sensing the rekindling of a real opportunity this week.

"Overall 68 out there is a really good score," he said. "I don't know where that's going to leave me at the end of the day, but I'm feeling pretty good that I've got a good chance going into [Sunday]."

At one over par, McIlroy was watching the scoreboard to see where Wolff would finish the day.

A startling 30 on the front nine took Wolff to five under par for the tournament at one stage.

"No matter where I am at the end of the day, I feel like I've got a pretty good shot," McIlroy said.

"You know, it doesn't take much around here ... someone gets off to a decent start, maybe one or two under through five and then the leader goes the other way, one or two over through five, and all of a sudden you're right in the thick of things."

Asked what conditions he would want on Sunday, McIlroy said: "It's sort of a double-edged sword, right, because you would think that you'd want tougher conditions because it'll make it more difficult for the guys in front of you, but it also makes it more difficult for yourself.

"I think looking at the forecast, the conditions are going to be pretty similar to today, which is fine. If I go out there tomorrow and shoot another 68, I won't be too far away."

He was full of admiration for Wolff's front nine, describing his scoring as "awesome golf".