Wilder needed just 137 seconds to knock out Dominic Breazeale and retain his WBC heavyweight title on Saturday, improving his record to 41-0-1.
The American drew with Tyson Fury in December and there were calls for a rematch with the Brit or bout against WBA, IBF and WBO heavyweight champion Joshua.
Wilder – whose knockout of Breazeale was the 40th of his career – said a fight with Joshua would happen, but he remains unsure when.
"The great thing about this is all these fights are in discussion, no doors are closed, all teams, all parties that are involved are talking and that's the great thing about it," he told Showtime.
"We know when the big fights happen everything is going to be silenced. There's too many people involved, too many opinions involved right now.
— SHOWTIME Boxing (@ShowtimeBoxing) May 19, 2019
"It's going to take my team and his team, maybe me and him as well, to sit down and hammer this and squash everything and get this fight done for the fans."
Wilder added: "This fight will happen. The big fight will happen, I promise you that, with patience, come time, and I just want you guys to have patience and give us a little time to make this thing happen so we all benefit from it, not only just you fans.
"We risk our lives in here so we want to make sure we get the best and the most money that's possible.
"We're risking our lives. The head is not meant to be hit in the first place so let us get our time to iron out all the differences and you guys will know when that happens."
Photo Getty Images. Caption: WBC heavyweight champion Deontay Wilder