Anthony Joshua's hopes for an undisputed world heavyweight title fight were put on hold when Wilder revealed on Wednesday morning that he would next defend his WBC belt against Ortiz, a decision described as "embarrassing" by promoter Eddie Hearn, The Independent reported.
Fury is the only boxer that Wilder has faced and not defeated, after the pair battled to a draw in December in Los Angeles.
Fury controlled much of the fight only to be knocked down twice, including one in the 12th round that looked to be the deciding blow.
"Luis Ortiz is first then Tyson Fury next," Wilder said on Twitter.
Wilder, who knocked out Dominic Breazeale in May, added in a separate tweet, "All contracts have been signed already?? It's officially on."
Neither Fury, who will take on Tom Schwarz in Las Vegas on June 15, nor anyone from his camp, has so far confirmed the Wilder rematch.