The 25-year-old French goalkeeper will enter the final year of his contract at Lille in the summer and is planning to move on from the French club at the end of the season.
Tottenham are interested in Maignan ahead of the transfer window and the club are claimed to have identified him as the long term replacement for Hugo Lloris.
But the Frenchman’s signature is set to be much-coveted as several clubs are interested in snapping him up.
According to Italian daily Gazzetta dello Sport, Maignan has climbed to the top of AC Milan’s shortlist of goalkeeping targets as well.
The Rossoneri are trying to convince Donnarumma to sign a new contract, but are afraid that the Italian will leave on a free transfer this summer.
Maignan is one of the names, alongside Atalanta’s Pierluigi Gollini and Udinese’s Juan Musso, on AC Milan’s radar.
But it has been claimed that the Lille shot-stopper is at the top of the pecking order of AC Milan’s goalkeeping targets.
Lille are believed to be eyeing a fee of around €25m from the potential departure of Maignan in the summer.