The British heavyweight, the owner of three of the four world belts, has been accused by some fans of the fight to break down the big match-ups, while rivals Wilder and Fury have had an emotional brawl in Los Angeles over the weekend.
Fury calls Joshua a "chicken" and a rematch between him and Wilder seems inevitable in the wake of their controversial draw.
This could mean that Joshua has been frozen by the division's best fights for a while, but the 29-year-old believes he is ready to go.
After Wilder's co-manager Shelly Finkel suggested that a Wilder-Joshua showdown could happen, Joshua wrote on Twitter: "What took so long?
"However well done Fury! They (Wilder) wanted to reach you because they thought you had finished !! I'll give you a nice one when you're ready, or one of you!"
The promoter of Joshua, Eddie Hearn, went to Los Angeles this week and says he hopes to talk about an April date between his fighter and Wilder.
Fury's promoter, Frank Warren, however, hopes to open talks on Fury-Wilder II.
Hearn told the Daily Mail: "First we need to find out what's going on with a Wilder-Fury rematch and if the rematch clause we're talking about is what it looks like.
"If anything, the way it ended Saturday is in our favor in terms of Wilder: it has always been the fight we want because it has the last belt.
"It could also happen that Wilder believes in his chances in a punch-out with AJ rather than in another at Fury. As for AJ, he will fight against anyone, he would like Wilder and he always wanted Fury.
"I'm going to Los Angeles and we're going to talk (with the representatives of Wilder) this week: it's a fight that we absolutely want in April and we will work hard to do".