Fury, 32, agreed to face Joshua, 31, in Saudi Arabia.
But Wilder's team forced an arbitration hearing which concluded he had a contractual right to face Fury for a third time. The latest fight is set to take place in Las Vegas on 24 July.
"There's no chance he [Wilder] will step aside," Arum told Boxing Social.
"Whatever it is, the judge said he had a right to the rematch and we are going to go ahead with it."
Arum said Fury was angry when he learned that the fight against American Wilder will take place, adding: "It is what it is.