UFC lightweight champion Conor McGregor claims he has signed his half of a deal to fight former five-weight boxing world champion Floyd Mayweather.

There have been rumours of a proposed bout between the Irishman and Mayweather since late 2016 following McGregor's win over Eddie Alvarez to become a two-weight UFC world champion.

“The first and most important part of this historic contract has now officially been signed off on," McGregor, 28, told themaclife.com. "Congratulations to all parties involved."

He said the emphasis was now on 40-year-old American Mayweather and his advisor Al Haymon.

UFC president Dana White confirmed McGregor had agreed terms and that any meeting with Mayweather would be "straight up boxing" rather than any mix with MMA.

"I'm starting to work on the Mayweather side now," said White.

"If we can come to a deal with Haymon and Mayweather, the fight's going to happen."

Many from within boxing have questioned whether McGregor could compete with Mayweather, who retired unbeaten in September 2015 after 49 professional contests.

However, many of McGregor's social media posts in recent months have shown him boxing and White stressed his fighter wants two bouts in 2017, one in the UFC and the other a meeting with Mayweather.

On Wednesday, Mayweather did not reference any communication between each side of the negotiation but said McGregor was the only opponent worth coming out of retirement for.

"There's only one fight that makes business sense," Mayweather said. "I came out of retirement because I'm a businessman and I want to give the world what they want to see.

"McGregor's a fighter, I'm a fighter. This is what the fight fans and MMA fans want to see."

Any bout is expected to generate huge revenues. Mayweather's 2015 meeting with Manny Pacquiao of the Philippines sold over four million times on pay-per-view, while McGregor's past three fights have passed the one million buys mark.