The Chilean's future has been a hot topic of conversation, with numerous reports circulating that Premier League side Manchester United were set to break their transfer record to secure his services.
However, Allegri, who replaced Antonio Conte as boss of the Bianconeri, has poured cold water on the rumours.
Allegri told the club's official website: "Vidal is fundamental for Juventus and not just in practical terms.
"He is very motivated and he is happy to stay."
The former AC Milan boss revealed he had met with Vidal to discuss his fitness, with the 27-year-old undergoing an operation on his right knee towards the end of last season shortly before competing in the World Cup in Brazil, where Chile were knocked out of the last 16 by the host nation on penalties.
"I spoke to him to satisfy myself of his physical condition as he was operated on and then played a World Cup, so he will train on a special schedule for a few days," Allegri added.