Mayweather extended his perfect professional boxing record to 50-0 with a 10th-round TKO of McGregor in 2017.
According to The Sun, the pair are currently in talks over another money-spinning fight.
A source claims that personal terms have already been agreed between the two fighters but there is yet to be an agreement over the number of rounds, with former UFC champion McGregor wanting 10.
The fight is set to be at 155lbs which would require McGregor to lose a significant amount of weight.
The Irish fighter is believed to have bulked up to around 190lbs since recovering from a broken leg which he sustained in his defeat to Dustin Poirier at UFC 264 in July of last year.
Mayweather has reportedly offered McGregor $157.9million (£131.5m) for the rematch and is said to be willing to put his unbeaten professional record on the line.
A source 'close to Mayweather’s camp' told The Sun: "Connor will only take the fight providing Floyd is willing to put his professional record on the line - so the fight will not be an exhibition, it will be an official fight.
"It will be at 155lb. That's what we know so far. It will be the last time Floyd ever steps in the ring so it is not one to miss.
"The deal is very close to being done. Personal terms have been agreed on both parties. It will be one final show down. And yes records will be at stake.
"Floyd sees it as the end of the Mayweather era and the beginning of the Gervonta Davis era.
"He believes it will be the biggest night boxing will have ever seen and has been saying 'People best be ready because it's going to be something spectacular'.
"There are arguments about the rounds at the moment with Connor's team wanting 10 rounds. But the deal and rights are certainly getting there."
The first fight between the pair, which was staged in Las Vegas, was the second highest pay-per-view event in history, attracting more than four million viewers.
Mayweather earned a reported £250m from the fight, with McGregor making more than £100m.
Mayweather has not fought professionally since that win, although he has taken part in three exhibition bouts against Tenshin Nasukawa, Logan Paul and most recently Don Moore.
McGregor returned to MMA after facing Mayweather but has won just one of his four fights since returning to the octagon, with his last appearance ending in a defeat to Poirier in their trilogy fight last July.