Fury, 30, registered a unanimous points victory over Francesco Pianeta on Saturday in only his second fight since returning from a two-and-a-half year spell out of the sport.
Fury seemed to confirm the bout between the pair will take place in Las Vegas, but promoter Frank Warren said all will be made known next week.
"We are two men who will fight anybody", Fury said of Wilder.
Tyson Fury says he has signed the contract.
"Fury against Wilder would be over in three rounds, at the most". "He's undefeated. They understand that", said the 66-year-old.
"I'll see you's in Vegas".
"They called. I answered", he said.
"I can't wait to fight you because I am going to knock you out", Wilder said to Fury.More news: Sports Direct wrangles with House of Fraser suppliers
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Although Wilder and Fury remained largely cordial during their face-off, with Fury even holding up Wilder's WBC belt and waving it to the crowd before handing it back, the brash Englishman of Irish Traveller broke character when he predicted how he would defeat Wilder before leaping into his face and bumping him.
With neither fighter doing any real damage, Fury maintained control of proceedings and finally landed a heavy left to the body in the seventh round.
Who will prevail when the current world heavyweight champion, Wilder, takes on the lineal heavyweight champion, Fury? It is on. This fight is official.
Speaking post-fight, Fury explained that he "needed the rounds" to get back to the desirable level he wishes to fight at. "The 6'9" heavyweight-regarded as the lineal World heavyweight champion following his upset win over Wladimir Klitschko in November '15-was light on his feet but sadly also with the impact of his punches, more interested in boxing that delivering an explosive performance.
"I don't think he'd ever beat Wilder".
The showdown will be arguably the most buzzed about heavyweight fight on American soil since Lennox Lewis squared off with a depleted Mike Tyson in 2002. I thought that was a step up in opponent and a great boxing display.
"I got 10 rounds with a very tough man under my belt". Styles make fights but when you're talking about Wilder, no-one knows what he is going to do - because he doesn't know either.