The Bianconeri's new coach has insisted the player is happy to remain in Turin after returning for pre-season training and also denied having any problems with Andrea Pirlo
Bianconeri chief executive Guiseppe Marotta stated on Monday that the Chile international would only be sold is he expressed a desire to leave Turin but the midfielder insisted last week he is not going to Old Trafford.
Goal understands Vidal met with his agent and senior officials on Sunday evening to discuss the possibility of a transfer to Old Trafford but Allegri has ruled out a move following a training session on Tuesday.
"Arturo is staying," the Juve coach told reporters. "He is very happy to remain here, like all of his team-mates.
"I have also spoken with him to check his physical condition. We are very happy that he's staying with us; he's fundamental for us."
Meanwhile, ever since Allegri was confirmed as the surprise successor to previous coach Antonio Conte, it has been speculated that the new boss could have problems with playmaker Andrea Pirlo.
The pair worked together at AC Milan and have conflicting views on the reasons behind the midfielder's free transfer from San Siro to Turin three years ago.
However, Allegri claims that there is no residual animosity between the pair, insisting that they are united in their desire to see Juve crowned champions of Europe.
"We spoke 10 days ago," the 46-year-old revealed. "We are professionals.
"There's a mutual respect between us and we have a common goal in wanting to have a great Champions League campaign. Europe has a particular fascination for us."
Allegri, of course, was sacked by Milan in January of this year and he has been handed a rapid return to San Siro by the newly-published Serie A fixture list for the 2014-15 season.
However, he insists that he has no fears about going back to the Giuseppe Meazza in week three.
"It will be a special evening for us and I will have many emotions," he confessed. "But now, for me, the Rossoneri are only another opponent."