Billy Joe Saunders is on the brink of agreeing to face Saul 'Canelo' Alvarez with "everyone in the right lane to make the fight happen", according to Jamie Conlan from his management MTK Global.
The fight would be in Las Vegas on May 2, the weekend of Mexican national holiday Cinco de Mayo, but could be at either middleweight or super-middleweight.
"It is getting very likely that it will get done," Conlan told Sky Sports.
The opportunity to face Mexican boxing's poster boy Canelo is one of the most glamorous in the sport, and Saunders was included alongside fellow Brit Callum Smith on the short-list for his next fight.
Last week their promoter Eddie Hearn confirmed with Sky Sports that initial offers from Canelo's promoters Golden Boy to both Saunders and Smith were not accepted.
"Not knocked it back, we just negotiated better terms," Conlan explained. "Billy Joe is in the pole seat. We believe everyone is on the same side in terms of what fight needs to be made.
"It's highly likely that the fight will be made. There are still some issues to be ironed out.
"Both fighters want it, both camps want it, everyone seems to be on the same side, we just have to hit the right number.
"They gave an initial deadline but the negotiations are at a point where there is no point backing out now.
"We're nearly there."
Canelo knocked out Sergey Kovalev to win a world light-heavyweight championship in his most recent fight, is a veteran of two classic middleweight battles with Gennadiy Golovkin, and his only loss in 56 fights came against Floyd Mayweather in 2013.
He has held major belts in four divisions but it was anticipated that his next fight would be to target a reigning super-middleweight titleholder to firm up his grip of that division. Saunders (WBO) and Smith (WBA) hold gold at that weight.
Canelo and Saunders have each been world champions at middleweight and super-middleweight and are still negotiating at what limit to meet.
"He believes he has the style to beat Canelo," Conlan said. "Everyone at MTK believes he has the style to beat Canelo.
"It's an interesting fight - the biggest of his career, the biggest of his life. We just need to make sure everything is right from his side."
Saunders, undefeated in 29, previously told Sky Sports: "I would take pleasure in ruining Cinco de Mayo for the Mexican fans."
Conlan has now warned: "Movement is a big factor. Austin Trout and Erislandy Lara gave Canelo trouble but weren't able to close the deal. Outside of Mayweather nobody has been able to figure out that puzzle.
"Billy Joe has always been a man in the division that you don't want to meet because he is stylistically opposed to what you want to be fighting. He can move, box, fight on the inside. When his mind is on the game he's one of the best in the world and he's proved that at different weights.
"Canelo needs someone to stand in front of him flat-footed. Amir Khan showed speed to give him problems, Lara showed [foot speed] to give him problems. Mayweather held the key to beating him but he was young and inexperienced - now he's seasoned and is the money-man outside of the heavyweights.
"It is a hard ask, the ultimate task for Billy Joe. But it's a fight that he has all the capabilities of winning."