The WBC heavyweight champion has given Joshua until Monday to sign the contract for the long-awaited British grudge match.
"We'll know by Monday anyway because if it's not done by Monday, I'm moving on," Fury said via Queenberry Promotions. "I'm not waiting around for some guy who's lost three of his last five fights.
"He's lucky I'm giving him a world title shot, but I don't mind chucking him a bone, you know, but I don't want them to start dictating s*** to me. He is an invited guest at my party, my rules, so if you want to play the game, come to the banquet and take your seat."
At the beginning of September, Fury challenged Joshua to a fight. Joshua quickly accepted the terms with his promoter, Eddie Hearn, saying he received the contract last week.
Fury last fought in April, stopping Dillian Whyte. Joshua last competed in August, losing a close decision to three-belt heavyweight champion Oleksandr Usyk.