Floyd Mayweather -- Invites 2 NFL Rookies ... For Private Gym Workout

Floyd Mayweather has taken 2 highly touted 1st round NFL draft picks under his wing -- and shut down his personal gym in Vegas to put them through his legendary training regimen ... TMZ Sports has learned.

We've learned ... San Diego Chargers running back Melvin Gordon and Minnesota Vikings cornerback Trae Waynes spent 3 days in Floyd's TMT gym in Vegas over 4th of July weekend.

Gordon's rep tells TMZ Sports ... the NFL players (who were high school teammates) met Floyd a few months ago and they hit it off ... so Floyd offered his place up as a training facility.

"Mainly they focused on conditioning," Gordon's rep tells us ... "they ran the treadmill and worked out two hours each day. They even hit the boxing bag a few times."

Floyd was out of town during the training sesh -- but we're told the guys plan to meet up with Floyd for more mentoring and training advice before the season starts.