Wilder, on the other hand, has traditionally fought on American rival Showtime. "ESPN and Top Rank are insisting that they want to give Tyson an exposure fight in the United States first, and then go to this fight [against Wilder] afterwards".
It could make future negotiations with American Wilder more hard, given he is aligned with the Showtime network.
Fury is planning an interim fight before he rematches Deontay Wilder and the pair are likely to come to blows this summer.
DuBoef declined to comment further to ESPN.
Fury said the two would "100 per cent" meet again in the ring but Wilder said he doesn't want to fight anybody else before a rematch.
The World Boxing Council subsequently confirmed that the rematch between the heavyweights wouldn't occur next, "while Wilder confirmed his willingness to fight the rematch, Fury will take on another fight with expectations to do rematch at a later date".
The rematch was fully expected to go ahead when the WBC officially ordered it to happen next.
Fury posted to social media Tuesday afternoon.
Prince William and Kate on royal visit to Northern Ireland
The royal couple were earlier given an official welcome to the venue by Lord Lieutenant of Belfast Fionnuala Jay-O'Boyle. The Youth Village, which sits on the shores of Lough Erne, caters for young children from across the island of Ireland.
"You sorry muthaf--. We knew you only said this [because] you knew you wasn't fighting me next", Wilder wrote.
"You requested a warm-up fight first", he said on Twitter.
"Get your self a bit more well known in America first kid & then I'll give you another chance.!", the Englishman tweeted. I don't blame you tho, I probably would too if I saw my brains splashed all over the canvas'.
A second fight has been anticipated since their first meeting in December, in which Wilder retained his belt after an enthralling draw in Los Angeles.
Fury's decision also leaves Dillian Whyte in limbo after the Brit opened negotiations with Breazeale for a summer clash.
Top Rank chairman Bob Arum said after the signing that he would send Wilder's team "a tremendous offer" for a multifight deal that would include a rematch with Fury later this year.
'It's unfortunate but we're hoping to get a fight in September or October'. So, in the meantime, we will do our own fight.
Judge Robert Tapper scored the fight 114-112 for Fury, while Alejandro Rochin favored Wilder 115-111.