La Gazzetta dello Sport says the France goalkeeper, whose contract only runs until 2026, has rejected the Rossoneri's current offer.
Milan are offering a €1m increase to €4.5m net per season, while Maignan's camp are demanding €5.5-€6 million-a-year for him to re-sign.
The Frenchman moved to Milan from Lille OSC in 2021 and now wears the captain's armband.
This season, Maignan has made 46 appearances and kept 13 clean sheets.