The four-time Major winner struggled on day three managing four birdies but also producing two bogeys and a seventh hole double bogey in a round of 71.
It was McIlroy's lowest score over the three days that sees him head into the last day sharing 11th place at level par.
He's six shots behind the leading duo of Justin Rose (67) and Sergio Garcia (70) tied at the top at six under par.
The record catch-up in Masters winning history was in 1956 when Texan Jack Burke Jnr came from eight shots back to capture the Masters by a shot.
If McIlroy is to win and capture also the Grand Slam he will need to go really low and given he has yet to break 70 this year after earlier scores of 72 and 73.
Rory McIlroy has slim hope of Masters glory heading into the final round
There were just a few too many wasted opportunities
“I had some chances on the back nine I could have converted,” he said.
“I had a great chance on 11 and 14 and where I hit my drive on 13 and 15, I should be making birdie there. I was just in between clubs on both those holes and took the wrong one on both and left myself in awkward positions. That’s the way it is.
“This course is getting a bit trickier with the greens getting a bit firmer. Pin positions were quite tough today. I think I probably could have shot a 67 or 68 but there were just a few too many wasted opportunities.
“But looking at the board I’m going to need – my best score round here is 65 and I’m going to need something like that if not lower to have a chance tomorrow.
“I’ll be able to tell you better tomorrow night if I think those missed opportunities have ruined my chances, but I just need to go out and play a good round of golf tomorrow.”
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Masters 2017: Dustin Johnson withdraws from tournament
Thu, April 6, 2017
Click to reveal the first snaps as Dustin Johnson withdraws from the Masters 2017
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Click for the first snaps as Dustin Johnson withdraws from the Masters 2017
A look at McIlroy’s scorecards over the three days he’s posted 11 birdies, nine birdies and the one double bogey today at the seventh.
In contrast, Rose has recorded 16 birdies and 10 bogeys while Garcia, and looking to win a very first Major on what would have been Seve Ballesteros’ 60th birthday, has 11 birdies, including four today, while the soon-to-be-married Spaniard has dropped just five bogeys.
“The mental side is huge and it’s the most important thing,” said McIlroy.
“Even if you aren’t playing well and your head is in the right place you’ll always have a chance. Around this place it is heightened even more because you can hear what is going on around you, if someone has made a birdie or eagle on the back nine. The leader board changes and everyone reacts to that so you have to focus on yourself and block it out.
“I feel like I play as aggressive as anyone round here. It hasn’t done me much good yet! But it’s one of these courses where you get a bit too aggressive, miss it on the wrong side and you end up not with birdie but with bogey and that gets frustrating”.