Bidding on the Nike RZN Black "RORS" ball started at $1,000 and had worked its way to $3,137 by Monday morning.
"In the collecting world, this is what's called a 'dream piece' -- something that no one could ever expect would become available for sale," Green Jacket Auctions said on its website.
Green Jacket executives saw McIlroy heave the ball into the crowd after sinking his final putt to win the Open. They immediately took to social media, seeking the fan who caught the souvenir.
An online search led them to Lee Horner of Leeds, England, and the negotiations began.
The auction is scheduled to end Aug. 9.