Allegri replaced Vidal with Paul Pogba after 70 minutes of Wednesday's Coppa Italia quarter-final, which Juve won 1-0 thanks to a late goal from Alvaro Morata.
Reports surfaced in the Italian media that Vidal was unhappy with Allegri, a claim that the coach has denied.
"Fight between who? Between myself and Vidal? I was surprised to read about it on Tuttosport, I believe it was Tuttosport," he said.
"First of all the day after [the game] I didn't talk with the player because he was absent during training and that's because he had fitness issues to take care of.
"Also, during the game, he was substituted but then came back because he had to nurse a knee problem.
"Then granted, a player can be upset when substituted, it's part of the game, part of football.
"But no, there was no fight with Vidal simply because there was no need to clarify anything."
