Former unified world champion Fury and Wilder are due to due battle for a second time on February 22 after their first fight last December was declared a draw.
Wilder taunted the Brit by claiming he never wanted a rematch and is "running" as he prepares to face Luis Ortiz at the MGM Grand on November 23.
Fury hit back by stating he is gunning for the American after making a winning WWE debut against Braun Strowman last week.
"If I was afraid of you I wouldn't have fought you after having three years out of the ring and beat you in your own country - and you had to rob me and give me a draw," Fury said in a video posted on Instagram.
"I don't know why on Earth you'd think I'm bothered about you. Just get through your fight with Ortiz, do your own thing, stop using my name for relevance.
"You should be on 20 per cent but I'm giving you a fair share, because I'm a fair man.
"I don't ask for anything in this world, I work hard for everything. So, the thing is with you Wilder, crack on with your own business and I'll see you February 22nd to finish what I started.
"This time you're going to get smashed, you big bum dosser."
Photo Getty Images Caption: Tyson Fury