11:39 AM PT -- Sources connected to Floyd tell us ... Floyd rented out the entire Syndicate MMA gym in Las Vegas on Monday for a private workout session.

As far as the MMA training goes, we've spoken to multiple people and everyone is being VERY tight-lipped about what Floyd was working on inside the gym.

We obviously know he spent some time in the cage -- but no one will say if Floyd was doing actual MMA training or just getting his usual boxing workout in with a change of scenery.

FYI, a ton of legit pro MMA fighters train at Syndicate, including UFC Hall of Famer Forrest Griffin, Jessica-Rose Clark, Mike Pyle and Julian Marquez.

11:28 AM PT -- Conor has seen the video and offered up some thoughts ...

"Hahahaha very good. Keep up the good work my son. Yours sincerely, Senior."

Well, here's Conor McGregor's dream come true ... Floyd Mayweather stepped into an MMA cage in what appears to be another attempt to bait the UFC star into another fight.

Floyd posted the footage on social media Tuesday -- one day after he took a shot at Conor for his #MCM ... which Floyd dubbed, "Mayweather Crushes McGregor."

Both Conor and Floyd made a killing off their superfight in 2017 -- but McGregor says he wants his next fight to be in the octagon.

So, how would that go? Oscar De La Hoya just told us the other day Floyd wouldn't last 10 seconds with The Notorious.

But we'd all probably pay to see it anyway ... and Floyd knows it.