Yves Rossy is a former fighter pilot. He's planning to try the stunt on Friday morning, although he's still waiting for final approval from the FAA.
FAA spokesman Ian Gregor says a decision won't be made until Friday morning.
The 51-year-old plans to jump from a helicopter on the Hualapai Reservation. The reservation lies west of Grand Canyon National Park.
This would be Rossy's first U.S. flight in his custom-built suit, which carries four kerosene-burning jet engines.
Rossy has also crossed the English Channel by air.