Wilder and Fury fought to a draw in Los Angeles this morning as the American defended his title.
Now Wilder is hoping to re-open negotiations with Joshua over a potential unification bout.
The Brit has reserved Wembley Stadium for April 13, 2019 and that could be used to stage the Joshua vs Wilder showdown.
And the WBC belt holder is hoping talks go better this time around after failing to agree on terms earlier this year.
“I would love to go for the other titles,” Wilder said when asked if he would prefer Joshua or Fury next.
“I have always spoken about being one champion, one face, one name.
“I always wanted to unify the division and I feel the one who unifies the division will really bring boxing back.
“It is too small to have so many champions. That has always been my issue.
“I think it makes the heavyweight division much more interesting to have one champion.
“I would love to fight Joshua and I have been trying to fight him – it is no secret.
“But those guys have other plans so we will see what happens.”
However, Wilder would still be happy if his next outing was a rematch with Fury.
“I would be satisfied with either one to be honest,” he added.
“Me and Fury put on one hell of a performance tonight.
“I would love to go into a rematch but I would also love to fight Joshua. I think I am in a win-win situation.
“I know what the fans want and I am with the fans too.”
Wilder’s manager Shelly Finkel is expecting a call from Joshua’s promoter Eddie Hearn later today.
“We don’t know what is going to be next,” Finkel said.
“If this other promoter calls tomorrow like he said then we will hear. If not it’s fine.
“I believe the fight right now with Fury is a stronger fight. It is probably more logical to happen. He still dropped the guy twice.”