Khabib, 30, reckons this is the best way to please fans who are desperate to see the unbeaten stars clash.
Speaking to beIN Sports, the Russian said: “If we make a bilateral agreement with Floyd Mayweather, the fans will be pleased.
"The first match in the ring and the second in the cage, then this would be real. I want to test myself in boxing once, that's fair."
Mayweather has spoken of a possible switch to the UFC in the past when The Money announced he is training in mixed martial arts.
And the UFC president Dana White stated the only way Mayweather will fight Khabib is under MMA regulations.
White said: "Listen, if Mayweather wants to fight, come fight. You fight in the UFC. We're not boxing him. We did that once. That's over.
"You wanna fight? You come fight – a REAL fight."
Both Khabib and Mayweather have publicly said they want the fight and it still could well be on, with Khabib potentially in line to take on the American and have a rematch with Conor McGregor.
After beating McGregor earlier in October, the Russian called out the boxing superstar.
He said: "Hey let’s go Floyd, we have to fight now.
“50 and 0 verses 27 and 0, two guys that never lose. Let’s go, why not.
Mayweather responded saying: “Oh, we fighting!"
"I'm in the cheque cashing business. I mean, I’m my own boss so I can’t say what’s going on on Khabib’s end but on my end we can make it happen.
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