The 30-year-old has claimed he has held talks with General Secretary of the Russian Boxing Federation Umar Kremlev to discuss a bout against the American in his homeland.
Khabib called out the five-weight world champion after defeating Conor McGregor in Las Vegas – and now plans to fight the Notorious' former foe.
The lightweight champion believes the proposed clash against the 1996 Olympic bronze medallist could attract 100,000 fans at the national Luzhniki Stadium, and break pay-per-view records.
Uploading a picture of him and Kremlev to Instagram, he said: "Today a meeting was held with the General Secretary of the Russian Boxing Federation Umar Kremlev to discuss the fight with Mayweather.
"We want the fight to be held in Moscow in the legendary arena. We are sure that we will collect 100,000 viewers.
"And also set a world record for the sale of paid broadcasts. And, most importantly, in the corner will be my father."
His father had trouble entering America due to visa issues, where he was unable to watch his son in action against McGregor.
In a video directed to Mayweather, Khabib said recently: "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. Because in the jungle only one king, only one king."
To which Mayweather accepted his offer, but insisted it will have to happen on his own terms.
He said: "Oh, we fighting. I'm my own boss. 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."
While also adding: "He called me out so he gotta come to my world. I seen in the interview he [Khabib] said when he hit Conor McGregor he knocked Conor McGregor down.
"He said I didn’t knock Conor McGregor down. But, okay, so Khabib you got my leftovers.
"I’m Floyd Mayweather, I’m the A-side. You called me out, you come into my world. Once again, I don’t know no other fighter that has done the numbers that I’ve done."
But while Mayweather wishes for a fight to take place in Las Vegas, Khabib has ruled out a bout taking place there with the Nevada's State Athletics Commission withholding his pay.