The former world heavyweight champion, 29, fights for the second time since beginning his comeback when he meets Italian Francesco Pianeta at Belfast’s Windsor Park on August 18.
He has made little secret of his desire to fight either of the division’s world champions, Wilder and Anthony Joshua, and insists he and his promoter Frank Warren are ready to take advantage of the breakdown in negotiations for a Joshua-Wilder unification fight.
Fury will have fought only four unremarkable rounds, against Albanian Sefer Seferi, in little under three years by the time of his bout with Pianeta.
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Joshua fights Russia’s Alexander Povetkin in September, but there still remains hope terms will be agreed for him to fight Wilder in April.
The 32-year-old Wilder’s desire for a high-profile opponent and his increased value in the context of a fight with Fury could make an agreement likelier.
Fury said on social media: “I can confirm that me and Deontay Wilder are in negotiations, very close to being done.
“Negotiations are very strong for December, we’re almost done for this deal.
“I won’t be overlooking Francesco Pianeta.
“He’s going to give me the right fight and the right work to prepare me for Deontay Wilder.
“I’ll flatten him first and then Wilder, let’s dance.
“You’ve been dealing with Eddie Hearn and Joshua, but I’m a man of my word. If I say I’ll fight you, I’ll fight you.
“Prepare well, train hard, let’s get the deal done.
“I’ll knock Pianeta into next week, I’ll knock you spark out too.”
In a separate post, he then revealed the potential Wilder fight would take place in the United States, as the champion would prefer, adding: “Next stop Belfast, then after that it’s Las Vegas or New York.”
Fury is currently in training in Manchester with trainer Ben Davison ahead of his outing at Windsor Park.
Morecambe’s former English and Commonwealth featherweight champion Isaac Lowe has joined the camp ahead of his rematch with British champion Ryan Walsh on a date to be confirmed.