The Italian champions head to Old Trafford having recorded back-to-back wins in Group H, putting them two points clear of their next opponents in the table.
Allegri is expecting another tough battle against a United side who also had to settle for a draw at the weekend, Jose Mourinho's side conceding a last-gasp equaliser away at Chelsea.
"It will be a physical game, we will have to approach it with great concentration, manage the ball and set up well on a technical level to avoid one of the greatest dangers that they can bring us, namely high balls," he told the media.
"Manchester United are a strong team who have a very experienced coach, and tomorrow's game serves as a reminder that we must always remain in the game for 100 minutes.
"We must keep in mind not only our game against Genoa, but also what happened between Manchester United and Chelsea, who drew in additional time."
Juventus travelled to Manchester without Mario Mandzukic, the Croatian forward remaining in Turin after suffering a sprained ankle in training on Monday.
Allegri - who is also missing Emre Can due to a thyroid problem - is planning to counter United's physicality by matching them for numbers in midfield.
"I'm sorry there is no Mandzukic, though it is not anything serious with him," Allegri revealed. "I had already thought about playing with others in attack.
"We will probably play with a back four, because in midfield we will have to numerically match them."