McIlroy, who won the last of his four majors in 2014, finished in a six-way tie for fourth place in Tokyo three years ago and joked this week that he had never tried so hard to finish third in his career.
This time around, while Schauffele, Rahm and Britain’s Tommy Fleetwood will start the final round in the medal positions, McIlroy is joined in the chasing pack by the likes of world number one Scottie Scheffler and former Masters champion Hideki Matsuyama.
“I’m in a really good place in the leaderboard,” added McIlroy.
“I was really close to getting a medal last time in Tokyo, I’m in contention to try and get a medal this time around, and I’m excited for that opportunity.”
McIlroy, in his first action since missing the cut at the Open last month, is 10 under going into the final round after a 66 on Saturday that featured five birdies and no bogeys.
“I can’t complain too much, to play a bogey-free round today with that really being the gameplan,” said the world number three.
“I went out today to really try and limit the mistakes. I played the front nine incredibly well again, I’ve played that nine in three-under-par each day.
“I played the back nine a little better today which was nice to see.”