But after failed negotiations this year, Wilder has labeled Joshua and his team cowards and soured on the idea of ever facing Joshua.
After exchanging harsh words in the leadup to the fight, both men were full of praise for each other following the final bell and were eager for a rematch.
"It was what it was", Fury said.
'I just showed the world tonight, and everyone suffering with mental health problems, you can come back and it can be done. That's a good thing for the heavyweight boxing division. "Holding on to an undefeated record is not what makes this sport great".
"I don't know how I get up, I had a holy hand upon me today and that got me back", Fury said after the fight. "If you saw that in Rocky, you would say "pull back Sylvester Stallone, you can't go that far".
Wilder had Fury on the canvas twice, including a spectacular final round knockdown, but was unable to get the knockout victory he had promised to deliver at the Staples Center.
The Briton instead survived as the exhausted Wilder struggled to force another attack and the stoppage, meaning an immediate rematch will be next.
A hard right and a left hook from Wilder sent Fury to the canvas and he looked to be out, but he managed to get up, Undertaker style, and pop up to his feet before the 10-count to continue the fight. He freely admitted, "I was too anxious in trying to get him out of there".
"None were like Fury when it came to publicity and generating news stories and none were like Wilder when it came to finding punches and dropping people". But the Englishman also made Wilder miss constantly, particularly ducking under Wilder's big right hand with grace.
But Fury gradually grew in confidence, regularly taunting Wilder by throwing his arms up in the air or behind his back.
According to CompuBox punch statistics, Wilder landed 71 of 430 shots (17 percent), and Fury landed 84 of 327 (26 percent).
A year later, he vacated his titles, following an investigation into doping and a cancelled rematch with Klitschko. "I would love for [the rematch] to be my next fight".
"We gave each other all we've got", Wilder said. It doesn't matter to me where we do it.
"We want to do it again but we want to do it in the (United Kingdom)". Opinions were divided on the judges' decision, however, with some claiming that Fury was robbed of one of the greatest comebacks in history despite two knockdowns.