Fury had appeared to dominate the fight with his superior boxing skills - both BT Sport and Showtime had him well ahead of their cards - but he was the one who ended up on the deck twice in the fight.
If the Fury camp gets it wish, it would not be the first time that a United Kingdom football stadium has played host to a big fight, with Wembley having hosted the world title fight between Joshua and Wladimir Klitschko among others.
Fury's jab did a lot of damage and kept Wilder at bay.
"I really thought I had him out of there", Wilder said afterwards.
Los Angeles Lakers basketball star LeBron James wrote: "Man that was the funniest/craziest fight I've ever seen in my life".
"I don't know what he was watching", added Fury.
He still has the green belt but the world knows it belongs to Tyson Fury.
"Listen 100 per cent we'll do the rematch, but we're going to go away, recalculate, see what's going to happen, get back together", he said.
Other sportsmen paid tribute to the efforts of both fighters, with former England and Manchester United defender Rio Ferdinand saluting Fury for how he has dealt with his personal demons. "It could easily have been a riot there last night, but I calmed the situation down by not complaining about the decision". I never had it easy, I had to work for whatever I got. "I'll leave the audience to make up their mind".
The 6-foot-9 Fury spent almost every moment of the fight nimbly avoiding Wilder's punches in a masterful display - except for the two moments when the 6-foot-7 Wilder viciously knocked him to the canvas.
"With the two knockdowns I definitely won the fight", said the American. "We poured our hearts out tonight".
"It is no secret I have been trying to fight Joshua". A lesser referee could've called the fight.
The card also saw Luis Ortiz score an 11th-round knockout of Travis Kauffman and Joe Joyce get a first-round knockout win over Joe Hanks. "It was a great fight and let's do it again". But Fury managed to come through in the sixth, when his combinations caused some swelling around Wilder's left eye.
"One hundred percent we'll do the rematch".
- SHOWTIME Boxing (@ShowtimeBoxing) December 2, 2018Two great champions.
Turning to and looking into the camera, he continued: "Every body out there who has the same problems I've been suffering with - I did that for you guys".
"He didn't want it for a reason: because Deontay Wilder is the most fiercest puncher in boxing history, in heavyweight division history".
Fury struggled to generate consistent offense until a strong sixth round, likely costing himself early rounds. But 115-111 for Wilder is bad, just awful!
The morning after the fight, with the threat of destruction removed, Fury was able to speak more freely about his disappointment.