The developer of Apeiron at The Jockey Club submitted plans for a tower to the FAA last week.
Apeiron will rise 549 feet above sea level, or 540 feet above ground, if approved by the agency.
The 40-story tower will include 120 serviced residences ranging in size from 1,500 square feet to 4,500 square feet. A 90-room hotel is also included in the tower.
Former Ritz Carlton CEO Horst Schulze is one of the developers.