Floyd Mayweather jnr has a new rival for the best self-publicist in sport: UFC champion Ronda Rousey.

There isn’t a bigger figure in female sport than Rousey, thanks in the main to her role as a totem in the macho world of Mixed Martial Arts. She’s a star, she can fight and she’s become a cultural icon.

She got in a good jab a few weeks ago by wondering aloud how Mayweather felt to be “beat by a woman” (after winning an ESPN award) and has followed up by claiming she would beat him in an all-in fight.

Mayweather shot back snarkily:  “I’ve yet to see any MMA fighter, or other boxer, make over $300 million in 36 minutes. When she can do that, then call me.”

Hear the drumbeats across social media and see the publicists circling like vultures overhead and you sense that something may be in the works. Remember, for boxing – and MMA – the weirder the better.

We’ve had one-legged boxers, 50-year-old champions and even midgets fighting. A man against a woman seems a natural step in fighting’s often warped evolution.

Except it’s already happened.

Sixteen years ago former drug-dealer Margaret McGregor made history when she beat part-time jockey Loi Chow in a four-rounder in Seattle. It was regarded as a freak show and the Mercer Arena was packed out.

Rousey concedes Mayweather would beat her in a boxing match, but insists she would prevail in a MMA contest. Such a bout would create massive hype, although, not surprisingly, this path has also been treaded.

A few months ago Brazilian amateur Larissa Schroeder belted Fernando Lemos in an MMA bout.

Part of the reason Rousey’s threat has gained such a strong foothold in the public consciousness is because Mayweather is the most polarising individual in sport. He gets up people’s noses. Those same people would love to see him defeated, particularly by a woman.

There’s no boxer equipped to do the job at welterweight, so why not endorse the claims of a ferocious female who would likely chop him down in a no-rules fight?

The irony would be glorious: a man with assault and domestic violence convictions getting whipped by a woman.

Rousey’s grappling game would cause him endless trouble and she’d likely have him on his backside in seconds thanks to her excellent judo pedigree – she competed at the2014  Olympic Games.

Will it happen?

Probably not.

But, damn, it’s good to dream.