The Bolton-born boxer has not fought since he was knocked out by Mexican Canelo Alvarez in May 2016.
Khan has spent the last 17 months recovering from a hand injury, but he says he is keen to return to the ring soon.
Mayweather retired from boxing in August after winning the big-money showdown with UFC’s Conor McGregor.
The American hung his gloves up with a record of 50-0, but he is now being called out by Khan.
The 30-year-old took to Twitter last night and in a series of tweets accused Mayweather of lacking power.
“Floyd is a great fighter, I just have something he’s not faced, speed. Floyd knows I’m not one to back down,” Khan wrote.
“I know it’s been a year I’ve not fought due to hand surgery. I’m ready to make a comeback at 30 years of age.
“Say what you like Canelo was getting out-boxed. I was winning on the cards. He had power and caught me with a huge right. that’s boxing.
“Mayweather doesn’t have the power. In any fight I’ve never been out-boxed.
“A Mayweather-Khan fight would be a game of chess. My speed, movement and accuracy will cause him problems.”