Frank Warren will discuss plans for the rematch against Deontay Wilder with Tyson Fury this week.
The 30-year-old excelled on the occasion of his first fight in Las Vegas on Saturday evening when he stopped the previously-undefeated Tom Schwarz in two rounds at the MGM Grand to enhance both his popularity and his reputation as the finest heavyweight in the world.
He is scheduled to next fight in New York on either September 21 or October 5, and the lucrative rematch with dangerous WBC champion Wilder will then become the priority for the first half of 2020.
December's thrilling and controversial draw between Fury and America's Wilder has made a rematch one of the most sought-after fights in the world, but Fury since signing to work with US promoters Top Rank and on ESPN further complicates the political landscape that exists between them.
The 33-year-old Wilder is committed to Top Rank's rival Al Haymon and a separate broadcaster in Showtime, but Fury's UK promoter Warren, who reached an agreement for December's fight before struggling to negotiate an immediate rematch, is confident they will succeed this time.
"There's a desire on both sides to get it done," Warren told Press Association Sport. "They're huge fights; they're the two best heavyweights out there, and there's a desire because there's unfinished business. Whatever way you want to look at it, even if Wilder thinks he won the fight, he was robbed.
"You know it's going to be a good fight, know that you get these two characters, a devastating puncher, probably the hardest punching heavyweight of the last 25 years, against the best heavyweight boxer I've seen in the same time.
"(In New York the opponent) will be somebody who's ranked in the top five and a step-up from Schwarz. Whoever it is will be selected with half-an-eye on Wilder.
"We need to sit down and have a discussion with Tyson, which is what we'll do in the next few days. He's just told you he wants the fight; everybody wants the fight.
"He's the best heavyweight in the world. He's the complete package. He's improving. He's only 30, not in his prime, and over the next four or fights will cement his legacy as the best heavyweight of his generation."
Fury's unusually destructive performance strengthened the argument of his trainer Ben Davison that he is continuing to improve, and the trainer added: "He's just turned 30, he's young, in form, and in shape now.
"I remember when (Floyd) Mayweather boxed (Oscar De La Hoya in 2007) and he said 'I'm done with the sport, what more can I achieve?'. But even then he went on, kept improving and tried to achieve more and more, and that's similar to where we're at with Tyson.
"(The next opponent) hasn't got to be exactly similar (to Wilder), but I don't want to make the adaption to somebody short then back to somebody tall again. There were elements I liked in there (against Schwarz); Tyson was just looking for something a little bit too much."