Fury and his team have consequently called for a rematch, yet Wilder appears to be again showing interest in facing Joshua.
Wilder's co-manager, Shelly Finkel says the American is "very interested" in putting his WBC belt on the line against Joshua, who holds the WBA, IBF and WBO belts.
Fury largely outboxed Wilder for the first half of the bout until a short right hand caught him on the temple and dropped him early in Round 6.
"I just showed the world tonight, and everyone suffering with mental health problems, you can come back, and it can be done".
Joshua has a Wembley date booked in for April 13, 2019, but with no opponent named as yet.
"You'd think they'd want the rematch, they've said they do." said Warren of Wilder's camp, with next Spring the rumoured target.
XFL announces eight teams, cities and stadiums for its return in 2020
Beyond the presser, the XFL posted a video with a list of the cities to its official Twitter account. "We pledge to bring St. Luck said they want more in-game rhythm and flow, and he also spoke about safety precautions.
"I am going out to LA and we will talk (with Wilder's representatives) this week".
With his fighter's reputation enhanced, Warren told Press Association Sport: "You'd think they'd want the rematch". I'll give you a fair one when your ready.
But Fury said that Wilder could try to avoid him.
"They said it was going to be a boring fight".
The previously-unproven Davison, 26, had been considered a potential weakness in Fury's preparations but in only their third bout together he oversaw a performance that suggests the fighter is again the world's finest heavyweight.
Wilder retained his WBC heavyweight title after the judges returned a split decision that earned much ire from pundits and fans, with most considering Fury the victor despite having to twice climb off the canvas. I don't know what fight those judges were watching; the guy who gave it 115-111, I don't know what he was watching.
Joshua last fought in September, when he successfully defended his belts by stopping Alexander Povetkin in seven rounds at Wembley.