The 22-year-old McIlroy overcame a collapse at the Masters in April to win the U.S. Open at Congressional this month by eight shots for his first major title.
Murray is hoping to put three previous Grand Slam final defeats behind him by winning the Wimbledon title to end Britain's 75-year wait for a men's singles winner here.
"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 against Wladimir Klitschko on Saturday.
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," he said. "Now that's been passed over to Andy. We're all behind him and hopefully he can win his first Grand Slam."