The PGA of America confirmed last month that a committee is studying the impact of holding the event outside the United States, with the earliest possible date in 2020.
It had been thought that Asia would be the most likely venue, but PGA of America president Ted Bishop told Golf Channel's 'Morning Drive' programme on Thursday that he was interested in Northern Ireland's Portrush.
"Royal Portrush would be a great first international major," Bishop said. "I think given the powerful effect that Irish golfers have on the professional game today, that might be a good place to start."
The R&A denied reports this summer that the Open Championship was set to be held at Portrush in 2018. R&A chief executive Peter Dawson admitted earlier this year that it is "a fantastic golf course," but concerns remain over the infrastructure required to stage a major and Dawson feels the current nine-course Open rota is "about right."
Portrush has not hosted a major championship since the 1951 Open, but the Irish Open drew massive crowds there in 2012.
McDowell, whose brother works at the club, said: "It's always been a dream of mine to play the Open there but the US PGA would do nicely.
"It's very bizarre and an amazing statement. I couldn't believe it and read it three times. I had heard the US PGA was looking at going global, which is a very positive step forward, but I was expecting Asia, not the north coast of Ireland.
"Even if it never comes to fruition it's a great boost to be mentioned in that breath. My brother Gary is on the greenkeeping staff there and he will have a spring in his step.
"Having three majors in America with the global nature of the game nowadays is a little too weighted. It's the fourth major of four so taking it somewhere else would really boost the interest. Asia, Australia or Europe would really embrace it."
McIlroy revealed the PGA of America had sought his views on the subject a few months ago, adding: "I spoke to Ted about it. He did not mention Portrush, just Ireland, but he has always liked Ireland as a venue.
"It's a long way down the road, maybe 10 years or so, but I would love to play a major championship at home.
"They (the PGA of America) are very forward-thinking and want to think outside the box. It's something the other majors have not done, they can't really go elsewhere. I think it's a good thing. It would be great to see.
"It would be huge. The Irish Open had a huge impact and everyone saw how well it was supported.
"Asia is the fastest growing region of the world in people playing the game and China are trying to produce the next Olympic champion so maybe down the line that will also be an option."