The Chilean’s future has been a hot topic of conversation with numerous reports circulating that 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 said: “Vidal is fundamental for Juventus and not just in practical terms. He is very motivated and he is happy to stay.”
One man likely to leave Old Trafford is Marouane Fellaini, amid reports the midfielder, who has endured a torrid time since joining the club for £27.5 million (€34.7m) less than a year ago, is on the verge of a transfer to Napoli.
What has yet to be determined is whether the switch will be permanent or a loan deal. But the player has met with representatives from Napoli and is pondering a move to the Italian club.
Napoli manager Rafa Benitez is rumoured to be a fan of the midfielder’s skills and believes his physicality would be an asset in Serie A.
It is understood United would prefer to sell the midfielder, even though any sale will likely be made at a sizeable loss.
United, meanwhile, have had to devise a special training programme to get Luke Shaw in shape for the start of the season.
Shaw, a £27m (€34.1m) signing from Southampton, had a fortnight off after the World Cup and he has arrived at United unfit, according to manager Louis van Gaal, who wants to see an improvement from the 19-year-old in the coming weeks.
“He needs to be fit and he is not very fit,” the United boss said.
“Therefore he cannot perform what I want so first he has to be fit and has to train individually. I have spoken with him and we have made the programme. He agreed with me.
“We will have to see how long it takes (for him to get fit).”
Van Gaal distanced himself from rumours of an imminent swap deal involving Javier Hernandez and Inter’s Fredy Guarin.
“I don’t know anything about it,” the former Barcelona manager said.
Van Gaal made the task ahead of Hernandez perfectly clear though.
“When he plays he will play in the striker position and he has competition with Rooney, Van Persie, Welbeck, Will Keane, Zaha — a lot players.”
One person who will not participate in the rest of United’s pre-season is right-back Rafael, who has been sent home to recover from a groin injury he suffered in training last Friday.
Van Gaal is sure the Brazilian does not require surgery, but he could not say whether he would be back for the first game of the season against Swansea on August 16.
“I don’t know (if he will be fit for the new season). We will wait and see,” Van Gaal said.