"I don't know if it will be the first one, but it will be on Fight Island, unless miraculously the world comes back together faster than I think it's gonna," White said on ESPN 1000 Chicago.
White said the infrastructure on the island is currently under construction.
"Hopefully it will be done by mid-June, and I could put on a fight that weekend that it's done or end of June," he said.
Gaethje won the interim title Saturday in the UFC 249 main event with a fifth-round stoppage of Tony Ferguson. Nurmagomedov was originally scheduled to fight Ferguson on April 18 in Brooklyn, New York, but as the coronavirus pandemic changed the card's location and fight lineup, Nurmagomedov said he was stuck in his native Dagestan and was replaced by Gaethje.
Nurmagomedov, who is Muslim, currently is observing the holy month of Ramadan, which this year is from April 24 to May 23. He trains during this time of fasting, but not at a level he would for a fight. He previously told ESPN he would need time after Ramadan to properly train.
"Any time Conor McGregor is fighting, it's exciting, but yeah, I'm very excited for Gaethje versus Khabib," White said. "I think stylistically it's a great matchup. I'm looking forward to it."