Chelsea made an offer for the 30-year-old in the mini transfer window ahead of the FIFA Club World Cup but saw it rejected by AC Milan.
Maignan was understood to be furious that the bid was rebuffed but has since had a change of tune and will remain at the San Siro.
Speaking to the media on Monday, Allegri said: "Maignan remains the captain and is one of the best goalkeepers in Europe. I am very happy he decided to stay."
The Frenchman has just one year left on his contract with the club and Chelsea could reignite their interest in January should he become available.