WBC heavyweight champion Wilder has long been talking with Anthony Joshua about a unification bout but, even with Wembley Stadium secured for the Briton for April, no contract has been agreed.
Eddie Hearn, Joshua's promoter, touted a fight between Wilder and Dillian Whyte at the weekend, too, but it now appears that the American will instead face Fury.
Fury (26-0) ended a two-and-a-half-year absence by beating Sefer Seferi in June and faces Francesco Pianeta in August, before turning his attentions to Wilder (40-0).