LONDON -- British golfers hold the top three spots in the world ranking, the first time that's happened in the 25-year history of the ranking.
"We've fed off each other's success," McIlroy told Sky Sports TV. "We saw Lee get to No. 1 in the world and Luke has been very consistent for the last two years. We're working hard to beat one another and strive to be better than everyone else."
Having started the year at No. 10, McIlroy overtook PGA champion Martin Kaymer without playing last weekend because of the German's poor showing at the BMW International Open.
McIlroy won the U.S. Open by a record score at Congressional on June 19. His next tournament is the British Open at Royal St. George's in Sandwich, England, starting July 14.
McIlroy says he wants to keep playing well while Tiger Woods continues his recovery from an injured left leg.
"It's a good time for me to win things when he's not playing his best," McIlroy said. "The first thing for Tiger is to get healthy and see what happens from there. I don't know if anyone can answer if he'll get back to where he was 10 years ago, but a lot of people would like to see him back on the course."
Woods hasn't won a title since the Australian Masters in November 2009. The 14-time major champion has plunged to No. 17 in the world rankings, his lowest spot since 1997. He is yet to announce whether he will be healthy enough to play in the British Open.