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|Brooks Koepka during the 2019 Open Championship at Royal Portrush AFP/Paul ELLIS|
"I've been out here for, what, five years. Rory hasn't won a major since I've been on the PGA Tour. So I just don't view it as a rivalry," Koepka told AFP ahead of his defence of the CJ Cup in Jeju, South Korea which begins on Thursday (Oct 17).
Second-ranked McIlroy's last major victory came at the 2014 US PGA Championship, while Koepka was still playing on the European Tour and yet to take up his PGA Tour card.
Koepka, 29, equalled the Northern Irishman's four-major total the US PGA Championship in May while McIlroy, 30, rounded off the season by winning the FedEx Cup for a second time and being voted PGA Tour player of the year.
McIlroy stoked the fires by saying he used a rivalry mentality to help him win the season-ending Tour Championship at East Lake at the end of August.
"He (Koepka) talked about trying to be the dominant player in the game ... and I thought: 'He's going to have to go through me first'," declared McIlroy.
"If that's both of our mentalities going forward, I think that's good for the game."
McIlroy is only the second player after Tiger Woods to win the season-long FedEx Cup race multiple times
As well as the Tour Championship-FedEx Cup double, his season also included victories at The Players Championship and the RBC Canadian Open.
But McIlroy did admit he had been a little surprised to pip Koepka to the Player of the Year accolade, voted for by their fellow PGA Tour professionals.
"I thought maybe Brooks winning the PGA Championship this year was going to be the difference-maker, but you know, the other players thought differently," he said.
Rivalry or not, they will lock horns next at the HSBC-WGC Championship in Shanghai in two weeks with the single-minded Koepka refusing to focus on anybody other than himself.
"I'm not looking at anybody behind me," said Koepka.
"I'm number one in the world. I've got open road in front of me I'm not looking in the rearview mirror, so I don't see it as a rivalry.
"You know if the fans do (call it a rivalry), then that's on them and it could be fun.
"Look I love Rory he's a great player and he's fun to watch, but it's just hard to believe there's a rivalry in golf. I just don't see it."