The 22-year-old McIlroy overcame a collapse at the Masters in April to win the U.S. Open at Congressional by eight shots this month for his first major title.
Murray is hoping to put three Grand Slam final defeats behind him by winning Wimbledon, which also would end Britain's 75-year wait for a men's singles winner here.
McIlroy met Murray and John McEnroe before the Scot's practice session. McEnroe asked McIlroy if he had any advice for Murray, who will play Feliciano Lopez in the quarterfinals Wednesday.
"Not really," McIlroy said. "He's playing awesome. He looked great yesterday. Keep doing what you're doing."
Murray wanted to know what McIlroy's upcoming plans were, and discovered the pair share a love of boxing. McIlroy, who will play at the British Open beginning July 10, said he would practice for three days before traveling to Germany to watch British boxer David Haye's heavyweight title fight Saturday against Wladimir Klitschko.
Murray, a boxing fan, struck up a friendship with Haye while they were training in Miami this year.
The 24-year-old Scot avidly watched McIlroy's U.S. Open win the night before Wimbledon began, but he downplayed his golfing ability.
"I used to play a bit when I was younger," Murray said. "My brother (doubles player Jamie) played really well. He played off like 3 or 4 (handicap) when he was 16. I'm more like 14, 15."
McIlroy didn't comment on his tennis skills, but said: "I'm a big tennis fan. I grew up watching Tim Henman here at Wimbledon and cheering him on every summer. Now that's been passed over to Andy. We're all behind him and hopefully he can win his first Grand Slam."