Evel Knievel, who died in 2007, failed to clear the chasm in 1974 in a rocket-powered "Skycycle" when the parachute malfunctioned and deployed after takeoff. Strong winds blew the cycle into the canyon, landing him close to the swirling river below.
Shawn Barigar, president of the Twin Falls Area Chamber of Commerce, told The Times-News that local government officials and business leaders have been invited to attend the private meeting with Knievel.
Julie Pence, spokeswoman for the city of Twin Falls, said officials are waiting to hear Knievel's proposal before commenting.
Robbie Knievel, a native of Butte, Mont., has been considering the jump for several decades, visiting the region in the 1990s to seek permission. But in 1993, he told the newspaper he wanted to "make sure everybody is happy about it first."
Local officials and businesses have been trying to use the site of Evel Knievel's jump to draw in tourists.
Last year the Twin Falls City Council agreed to make a change to a land trade agreement so the public could have access to the area.