CELEBRITY SHOWDOWN?: Singer Justin Bieber (above right) once traded punches with boxing champion Floyd Mayweather Jr (left) in a ring.

But that training was for fun.

The singer is in good shape physically, but can he go the distance in a real, competitive fight?

Fans may be able to find out, given that Bieber, 25, has issued a showdown challenge to actor Tom Cruise, 56.

Posting on Twitter on Sunday, Bieber wrote: "I wanna challenge Cruise to fight in the octagon. Tom, if you don't take this fight, you're scared and you will never live it down. Who is willing to put on the fight?"

It is not known why Bieber wants to take on the actor, who has done his own dangerous stunts in the Mission: Impossible movies.

But former mixed-martial arts champion Conor McGregor is keen to get the fight going.

"If Tom Cruise is man enough to accept this challenge, McGregor Sports And Entertainment will host the bout. Does Cruise have the sprouts to fight, like he does in the movies?" he posted another dare.

He runs the McGregor Sports And Entertainment events company.

If it does take place, pundits expecting a victory for Bieber will prove mission impossible.

It is a little-known fact, but Cruise was also in the wrestling team in his high-school days.