In a letter seen by Reuters, the FAA said it had "finished the necessary processing steps" after the Clark County Department of Aviation requested the change in April.
The request, which will change the name of McCarran International Airport to Harry Reid International Airport, has been "published in various flight charting and navigation databases," the FAA said in its letter dated Wednesday, but the county must update and submit additional regulatory documents.
Las Vegas was the seventh busiest airport in the United States by passenger traffic in 2020, according to FAA statistics.
An airport spokesman the process of changing the name will be divided into three phases.
"We estimate the combined cost of these phases will be approximately $7 million, all of which must come by way of private donations," spokesman Joe Rajchel said in an email.
He said it would be premature to provide a timeline for the project.
Reid represented Nevada in the U.S. Senate and House of Representatives and was the Senate Democratic leader for 12 years. He retired in 2017 after more than 30 years in Congress. Reporting by David Shepardson Editing by Sonya Hepinstall