John Elway's Longtime Agent Jeff Sperbeck on Life Support After Golf Cart Accident

Jeff Sperbeck, John Elway's longtime business partner, is in the hospital on life support ... following a horrific golf course accident over the weekend, TMZ Sports has learned.

We're told Sperbeck was at The Madison Club in La Quinta, CA on Saturday afternoon, riding on the back of a golf cart, when something went terribly wrong ... and Jeff somehow fell off the moving vehicle, landing on the ground, and hitting his head.

Jeff's wife and at least one other person noticed Sperbeck was down and quickly turned around to check on him. It was immediately clear the longtime sports agent was in bad shape, and someone called for help.

Sperbeck was rushed to Desert Regional Medical Center ... but sadly, the prognosis is not good.

Although Jeff's not clinically dead, we're told doctors have informed his family there's no hope he will recover ... and he's being kept on life support while docs prepare to harvest his organs for donation.

While Sperbeck isn't a household name himself, he was instrumental in the career of Elway, one of the greatest football players of all time.

John and Jeff began working together in the early '90s, with Sperbeck serving as his sports agent, business manager and business partner for over three decades.

Despite Elway's Hall of Fame career coming to an end in 1998, the duo remained close ... with Jeff and the former league MVP starting a winery together, 7Cellars, in 2013.