The Briton returned to the ring in June after a 32-month absence with a stoppage victory over Sefer Seferi at the Manchester Arena.
Fury, who is set to fight Italian Francesco Pianeta in Belfast on August 18, insists that a bout with America's WBC champion Wilder could follow in December.
"I can confirm that me and Deontay Wilder are in negotiations," the 29-year-old said in a video posted on Twitter. "[It is] very close to being done.
"I can reveal that negotiations have been very strong for December. We are almost done with this deal.
"But I won't be looking over Francesco Pianeta. He is going to give me the right fight and the right work to prepare me for Wilder."
Fury stunned Wladimir Klitschko in 2015 to land the WBA, IBF and WBO world titles.