The Nevada city has been considered a front-runner for expansion for some time, with Foley securing more than 13,200 season-ticket deposits for a multipurpose arena currently being constructed near the Las Vegas Strip.
Seattle and Quebec City are other markets that have expressed serious interest. A second team in the Toronto area leads the list of additional possibilities.
NHL commissioner Gary Bettman has said the expansion fee will be at least $500 million US.
On Monday, Quebecor applied for an NHL expansion franchise with the aim of bringing the Nordiques back to Quebec City after they left for Denver in 1995 and became the Colorado Avalanche.
The NHL has not expanded since adding its 29th and 30th franchises, Columbus and Minnesota, in 2000.
Deputy NHL commissioner Bill Daly has said the earliest any expansion would happen is the 2017-18 season.
In Las Vegas, MGM Resorts and sports conglomerate AEG are building a $350 million, 20,000-seat arena slated to open next year.
"We're going to take a deep dive and look at what there is in terms of the interest that's being expressed," Bettman said. "Obviously, Bill Foley got a great response to his season-ticket drive."
The expansion bidding process closes Aug. 10.
The NHL hasn't decided how many clubs it might add, and it doesn't anticipate expansion before the 2017-18 season.