Chelsea made an offer for the 30-year-old in the Mini Transfer window prior to the FIFA Club World Cup, but saw it rejected by AC Milan.
Maignan was considered furious that the bid had been rejected, but since then had had a change in the melody and will stay with the San Siro.
Talking to the media on Monday, Allegri said: “Melignan remains the captain and is one of the best keepers in Europe. I am very happy that he decided to stay.”
The Frenchman only has a year left on his contract with the club and Chelsea could accommodate their interest in January if he would become available.