Caitlyn Jenner -- Bruce CAN Be Erased from Olympic Hall of Fame ... If She Wants

Caitlyn Jenner can make Olympic history again -- the doors to the Hall of Fame are swinging wide open for her to enter ... all she has to do is ask.

Caitlyn was inducted into the H.O.F. back in 1986 thanks to her legendary gold medal in the 1976 Olympic decathlon. But, of course ... Bruce is the name attached to that honor. At least for now.

Patrick Sandusky, spokesperson for the US Olympic Committee, tells TMZ they would gladly update the name to Caitlyn. He says if she files a formal request, the Committee would review it, and presto -- bye bye Bruce, hello Caitlyn.

A rep for Caitlyn tells us she's unclear if she'll make the request.

She's got time to think it over. There won't be any physical honor for the H.O.F. inductees until the U.S. Olympic Museum opens in 2018.