The France international has signed a new deal with Milan to 2031.
Ahead of tomorrow's clash with Bologna, Allegri said this morning: "I'm very happy because Milan has secured one of the three best goalkeepers in Europe.
"He's very happy, he's always said he wants to stay, and the club did a good job of ensuring Mike stayed at Milan. Now let's focus on tomorrow."
"I didn't convince Maignan at all," Allegri added. "The credit, as it should be because they've worked hard and they decide on contracts, goes to the club. After Maignan stayed in the summer, I was confident he could continue at Milan.
"Maignan is a very sensitive guy, I knew he wanted to stay. All that was needed was to get over that misunderstanding in the summer ... And then he made saves!"