The 20-year-old says that he has learnt a lot from the Italian tactician and describes him as a "great coach".
"Allegri has given me so much and he has had three outstanding seasons with Milan," he told Milannews.it. "We have always been behind him, even when he has been questioned.
"He didn't listen to the criticism. He continued with his way of doing things. This year, we have made a real comeback and we have to be truly grateful to him because he has done a great job.
"I hope he stays with us. He's a great coach and we are very happy with him. There are so many rumours about him, questioning him, but I hope he remains here and believe that he will."
Allegri's current contract with Milan runs until June 2014.