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Boxer Claressa Shields To Amanda Nunes ... 'I'd Put You to Sleep'

The greatest female boxer in the world wants a piece of the greatest female UFC fighter in the world ... with Claressa Shields guaranteeing she'd KNOCK OUT Amanda Nunes!!!

"If we were to fight, I would win," Shields told us bluntly ... "In boxing, yeah, Amanda Nunes would go to sleep."

24-year-old Shields is a MONSTER in the ring -- she's 9-0 and the undisputed women's middleweight champion of the world! BEAST!!

Of course, Nunes ain't no punk -- she's widely considered the greatest female MMA fighter EVER ... after smashing everyone from Ronda Rousey to Cris Cyborg and Holly Holm

Sheilds says Nunes would obviously have the advantage if they stepped into the Octagon, but in a pure fistfight ... oh man, Sheilds says Nunes wouldn't stand a chance! 

So, could it happen? 

Don't rule it out ... Nunes prides herself on her striking ability and we've seen MMA fighters jump into the boxing ring before (McGregor vs. Mayweather anyone!?). 

In the meantime, Claressa says she REALLY wants a crack at welterweight champ Cecilia Braekhus, a 35-0 superstar who hails from Norway. 

Shields says she's been trying to set up the fight but Cecilia won't return her calls -- explaining, "Nobody wants a piece of me."

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