TMW says Milan are close to selling Maignan to Chelsea over the next 48 hours.
The Blues want to close a deal before Tuesday night's Club World Cup transfer deadline.
Chelsea's latest offer of €15m has been rejected by Milan, which are insisting on €25m to sell. A new proposal involving bonuses reaching Milan's price is now expected to be tabled by Chelsea.
Meanwhile, Tare has already identified Maignan's replacement in Torino goalkeeper Vanja Milinkovic-Savic.
Amongst a raft of candidates, Milinkovic-Savic is the option favoured by Tare.