Talks to agree a bout between Anthony Joshua and Tyson Fury for 2021 could take just â€œa couple of daysâ€ to be completed, promoter Eddie Hearn says.
Joshuaâ€™s knockout of Kubrat Pulev on Saturday has set up the prospect of a clash between the British rivals.
Negotiations start on Monday and it could be the first fight in history for all four heavyweight titles.
â€œThere is no reason we cannot complete the deal and then move on and solve the other problems,â€ Hearn said.
WBC world heavyweight champion Fury has been installed as an odds-on favourite to beat IBF, WBA and WBO belt holder Joshua if they fight next.
Asked how long realistically it would take to complete the deal, Hearn replied: â€œA couple of days.
â€œWe need to write to the governing bodies and say yes we have a deal and we will now talk to the various sites and confirm the dates shortly for what I suppose will be the end of May.â€
â€œI want the fight next. I canâ€™t wait to knock him out,â€ Fury said in a video posted on social media on Saturday night.
There are some potential issues, including if Fury is forced to fight Deontay Wilder for a third time, while Joshua could be told by the WBO to face mandatory challenger Oleksandr Usyk.
But Matchroom promoter Hearn added: â€œThe only hitch I can think of is Wilder. If the court orders the Fury rematch, and it doesnâ€™t sound as though they will, then it is out of our hands.
â€œThat is the only way it falls through is if something stops their side, that isnâ€™t me saying they donâ€™t want it, they do, but if the court orders it then we will have to fight Usyk.â€
If Usyk and the WBO do not agree to that title being on the line for Joshua-Fury, Hearn said they could vacate the belt in order to ensure one of the biggest fights in British boxing history is able to take place.
Hearn said: â€œIt is an undisputed fight, it should be the toughest fight out there, but Iâ€™ve always fancied him to beat Tyson Fury, always.
â€œBut Fury is definitely at the peak of his powers and so is AJ which actually is why it is so great if we get it made because you saw with Floyd [Mayweather] and [Manny] Pacquiao, it was rubbish.â€
Joshuaâ€™s trainer Rob McCracken said his fighter is â€œgetting better all the timeâ€.
â€œI would think they would definitely fight and probably fight at least twice next year, thatâ€™s what everybody wants to happen,â€ he said.
â€œBig Josh has had 10 or 11 world title fights and is still developing and winning. Heâ€™s getting better all the time.â€