"The Gypsy King" and UK promoter Frank Warren both hailed the new deal, but for many it has thrown into doubt a rematch between the lineal heavyweight champion and WBC titleholder Wilder.
"I want the biggest fights, the Joshuas, the Wilders of the world, and everyone else out there too".
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"The agreement will mean that Fury will be a headline part of the boxing lineup under the historic, long-termTop Rank on ESPN relationship".
Sulaiman hopes, also, for the victor to fight WBA, IBF, WBO and IBO champion Joshua to find the first undisputed champion since Lennox Lewis.
Some may argue the American has more to prove than Fury in a potential rematch having escaped with a draw.
Fury's promoter Warren insists the Wilder-Fury rematch remains likely, and the British fighter was adamant it is "more makeable now than ever" after signing his multi-year, multi-fight agreement with ESPN.
"If you're watching Deontay I'm coming for you baby and this time you won't rip me off".
Wilder refers to the proposed date, saying: 'I will still be ready for Fury on May 18'. "(Haymon) wants to make the fight and that whatever is realistic will get done". Showtime's not the only game in town. Wilder knocked Fury down twice in their first fight, and seemingly had him out in the 12th round, but Fury got to his feet and was fighting back at the end in as dramatic of a finish to a heavyweight title bout as there had been in decades. We'll get him out.
"(ESPN) will be Tyson's exclusive broadcaster in the States, and have a platform of almost three million.
He said at a press conference: "It gives him a chance to become the guy you want to fight now".