The former five-division world champion's promotional company, Mayweather Promotions, confirmed on Twitter he had made the offer, and several local media reports have said the family have accepted.
TMZ Sports tweeted a picture of a cheque from Mayweather to George Floyd's funeral service for $88,500.
Mayweather also paid for the funerals of Genaro Hernandez, his former opponent, and the legendary Joe Frazier in 2011.
Mayweather Promotions and the boxer's agency have yet to respond to a request for comment.
The Minneapolis police officer who kneeled on Floyd, Derek Chauvin, has been sacked and charged with third-degree murder and second-degree manslaughter.
Several high-profile sports stars, including Tiger Woods, Michael Jordan and Lewis Hamilton, have expressed outrage at Floyd's death
Three other officers involved in the arrest have not been charged.
The incident has prompted anger across the United States and abroad, with numerous professional athletes and leagues speaking out, including NBA great Michael Jordan and golf's 15-times major champion Tiger Woods.