Muhammad Ali's legacy ... is in Flavor Flav's hands -- 'cause the rap legend tells TMZ Sports he's managing Muhammad's grandson's boxing career!
Flav was out in Bev Hills with TV pitchman Ron Popeil -- when he told us all about his 15-year-old prodigy Nico Ali Walsh ... a rising star in the sport (check out video below, he's in white trunks).
"The boy is good," Flav tells us ... "That's all I gotta tell you, he's good. Come see the fight."
Flav says Nico's fighting in L.A. on July 30th.
Flav's also a huge fan of Nico's brother, Biaggio -- a big-time high school football star and model ... who also happens to be Flav's godson.
Check out the clip ... pretty cool stuff.