2:03 PM PT -- Here's video of Jay speaking to TMZ Sports about the situation ... and explaining why Hardy will NEVER be allowed to set foot inside of his gym. Greg Hardy doesn't deserve "the privilege" of competing in MMA and should be BANNED from the sport ... so says Jay Glazer who's calling for his fellow MMA coaches to blackball the ex-NFL star.
"I would be incredibly disappointed in any of my fellow MMA coaches and any promoters if they took Greg Hardy in and taught him a shred of our incredible sport," Glazer tweeted.
"Competing in any sport is a privilege, Greg Hardy should not be granted the privilege."
Glazer makes it clear his beef stems from Hardy's 2014 domestic violence conviction -- when he was accused of beating the crap out of his ex-girlfriend and threatening to kill her.
Hardy appealed the conviction -- and the case was dismissed when his accuser stopped cooperating with prosecutors.
"Many of us train women in self defense specifically to help protect vs domestic violence," Glazer said ... "Me and all my coaches at @Unbreakable do and take great pride in that."
"There are many beautiful arts taught in our sport, none of which should be afforded to him."
Glazer trains a bunch of huge MMA stars at his Unbreakable gym in L.A. -- including Luke Rockhold and Chuck Liddell.