Discussions took place between their teams on Tuesday night.
Both sides are keen to fight again after a dramatic draw in Los Angeles meant Wilder held on to his WBC title.
Next spring is the preferred date, with US and UK venues possible.
The WBC are set to meet in the coming days to discuss their position following the controversial outcome.
“I’m looking forward to giving him the rematch as soon as possible”
Fury’s promoter Frank Warren has written to request a rematch, with the British fighter’s camp unhappy with the judges’ decision.
They are confident the sanctioning body will mandate a rematch.
That will mean Wilder will not be allowed to defend the belt against anyone else next other than Fury, which would end hopes of Anthony Joshua facing the American in April.
But that is not expected to be a problem for the ‘Bronze Bomber’, who says he is ready to send Fury “back to hell”.
Wilder said: “I’m ready to do it again. My main goal is Tyson Fury.
“I’m looking forward to giving him the rematch as soon as possible.
“This is the biggest fight still in the heavyweight division, this is the most exciting fight in the heavyweight division and we’re ready to give the fans what they want to see.
“He woke up from hell – I want to put him back there. Both sides definitely want it to happen and I don’t see why we wouldn’t.
“It’s a great fight and the build-up has already started. We can’t get away from this fight.
“It’s only right for us to go back in and do it again.
“I don’t want no other fights to happen between him or I before then. I want to give Tyson Fury the rematch ASAP.
“It might even be a trilogy if the second fight is as good as the first.”