And Mayweather, a former pound-for-pound king who initially retired from the ring in 2015, confirmed on Saturday that he would only return to boxing for a showdown with the MMA fighter.
"McGregor is the only fight I will come back for," he said.
"That's 100 per cent. It's the only fight that makes sense to me.
"I've accomplished everything else. Is this one extra obstacle to overcome?"
The 40-year-old has been in the UK this week on promotional duties. He was at the Copper Box arena on Saturday to see his protege, Gervonta 'Tank' Davis, stop Britain's Liam Walsh and retain his IBF super-featherweight title in emphatic fashion.
Joshua, meanwhile, has been out of the ring since he rose from the canvas to beat Wladimir Klitschko in last month's epic heavyweight clash that cemented his place among the biggest icons in the sport today.
The 2012 Olympic champion is being touted by many to takeover the mantle as the leader of boxing from Mayweather, who won all 49 of his professional fights.
Mayweather, nicknamed 'Money', is one of the richest stars in sport and claims to have earned more than more than £610 million during his career. Joshua has aspirations to surpass the unbeaten American, however, claiming last month that he wants to become the world's first billionaire boxer.
And as well as sharing a video of him and Mayweather on his Instagram on Sunday, Joshua uploaded a photo of a signed boxing glove depicting the two 'unified champions' with the caption: 'A night to forget - TBE meets AJBXNG'.