McIlroy, 19, is this week bidding to become the youngest winner on the USTour. He was 11-under midway through the third round, four shots off the lead at the Doral Resort and Spa.
"The guy's a talent," Woods said of the youngster from Northern Ireland. "We can all see it, the way he hits the golf ball, the way he putts, the way he can chip, get up and down.
"He has the composure. He has all of the components to be the best in the world, there's no doubt.
"It's just a matter of time and experience in big events. That takes time and I mean, he's only 19," Woods said after finishing on 209, seven under.
The 33-year-old American, playing his best golf since returning from an eight-month layoff, birdied the par-five first hole before failing to convert a series of tricky birdie chances.
In all, Woods had seven lip-outs in his round.
After seven straight pars he finished the outward half with a birdie on the par-three ninth.
"I have not controlled the ball that well in a long time and that was fun," said Woods.
"I was hitting shots I had not been able to hit before which was such a great feeling. Unfortunately I am just not making any putts."
The world number one added three more birdies on the inward half, the highlight coming at the par-four 16th when he holed out from a greenside bunker.
That good work was undone on the next hole when Woods found a fairway bunker and his recovery hit the lip of the trap before ending up close to a tree.
An excellent third stroke found the green but two putts cost him a bogey.
Woods had been well off the pace at the start of the day after beginning his first strokeplay event since knee surgery with scores of 71 and 70.
"I am getting better each day, the feel of playing the game at this level is coming back," said the 14-times major winner.
"I had six lipouts the first two days and seven lipouts today for birdie, that's a lot and it is pretty frustrating."