"The ideal thing would be not only to keep hold of Vidal but to bring others in," Allegri told reporters.
"We have never activated a clause to try to sell him and if he doesn't show an intention to leave, our position won't change.
"He is a player that I consider fundamental and he wants to stay here," added Allegri, who took over from Antonio Conte earlier this month.
Vidal has been frequently linked to United during the close season, with media reports saying the Premier League club are preparing a 48 million ($81.30 million) bid for the 27-year-old.
He scored 11 league goals for Juve last season as they romped to their third straight Serie A title.
The Chilean played down speculation of a move on his return to Italy after the World Cup and Juve's sporting director Giuseppe Marotta said the club would not sell unless Vidal made clear his intention to go to England.
"We don't want to sell Vidal, there are only rumours because he is among the best players in the world," Marotta told Sky Italia.