The Northern Irishman carded an excellent 68 on day three to go with an opening 67 but those two rounds sandwiched a 76 which left him at one over.
American Matthew Wolff was in the box seat at five under after a stunning 65 that matched the lowest round of the week in tougher conditions than on day one.
But the West Course at Winged Foot Golf Club is regarded as one of the toughest tests in golf and McIlroy knows there is plenty that could happen over 18 holes as he looks for his first Major win in six years.
"I still don't think that's out of it by any stretch of the imagination," he said of his position.
"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.
"We'll see what happens. No matter where I am at the end of the day, I feel like I've got a pretty good shot.
"If I go out there tomorrow and shoot another 68, I won't be too far away."