Wilder (40-0-1) floored Fury (27-0-1) in the ninth and 12th rounds yet Fury clearly outboxed Wilder for large portions of the remainder of their entertaining showdown at Staples Center on Saturday.
Fury controlled proceedings and looked the superior boxer, but could still have left with nothing after Wilder knocked him over on two occasions.
"If it's a great fight and fans want to see the rematch then why not?"
"That man is a fearsome puncher and I was able to avoid that. Me and this man are the two best heavyweights on the planet".
Wilder almost stopped Fury in the 12th round with a hard knockdown, but Fury survived and stormed back for a memorable round of the year candidate in a fight that is likely to see a sequel.
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. Wilder tried going to the body too but, more often than not, his punches landed harmlessly on Fury's massive elbows.
Still, the knockdown scuppered his hopes of becoming a two-time world champion, with the controversial outcome seeing both retain their unbeaten record while also paving the way for a lucrative rematch in 2019.
Fury raised his hands at the end of the 11th, though his celebrations appeared premature when he was dropped again, a right hand doing the damage before a left hook caught him flush while already on the way down.
But Fury gradually grew in confidence, regularly taunting Wilder by throwing his arms up in the air or behind his back.
Wilder however suddenly found a devastating combination just when he needed it in the 12th round.