The Bianconeri manager believes it is only natural that such a world-class talent is the subject of so many rumors but insisted that the Chile international will remain in Turin.
The Chilean has been heavily linked with a transfer to Old Trafford since this summer's World Cup but his coach believes that rumors of an imminent move away from Turin are merely representative of the fact that the former Bayer Leverkusen man is a top player.
"I don't think he's on the market, if that's what you want to know," Allegri told Tuttosport. "Great players are always talked about. Big clubs are only looking for great players, but Juventus are a great club. Obviously Bayern or United or Real Madrid can think about him as much as they want."
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The former AC Milan coach went on to say that he will not be rash in the transfer market as Juve looks to further strengthen its squad with a couple of additions before the start of the new Serie A season at the end of the month.
"I'll assess things with the club," Allegri said. "We have little time and the margin for error is thin. If we bring in two players, we cannot go wrong. We will evaluate what to do in the market in the attack.
"It's better not to sign anyone that someone who's not needed. It's useless if we sign a low-level player. If we sign one, it'll be a major player. We need a player who can play in both formations we use, the 3-5-2 and with three strikers."