The Stamford Bridge hierarchy previously failed with an opening proposal for the France international when he was entering the final year of his previous contract.
The 26 year-old goalkeeper was highly receptive to moving to the Premier League at the time and had reportedly finalised terms on a potential contract.
That initial deal collapsed entirely after the Italian side demanded a much higher fee than the west London club were willing to pay.
Maignan subsequently committed his long-term future to the Serie A club by signing a lucrative contract extension that runs until 2031.
The experienced goalkeeper remains open to securing a transfer away from Italy following the recent departure of manager Massimiliano Allegri.
The English club have already initiated contact with the player's representatives to determine if an agreement can be reached this summer.
Chelsea officials have held discussions with the goalkeeper's primary agent Jonathan Kebe to establish the parameters of a potential deal.
The Premier League club have yet to submit a formal financial offer to their Italian counterparts during this initial exploratory phase.
New Chelsea manager Xabi Alonso remains determined to secure a high-profile upgrade to his options between the posts ahead of next season.
The London club will face significant resistance from new AC Milan head coach Ruben Amorim who views the goalkeeper as a fundamental cornerstone of his project.
Amorim is extremely reluctant to sanction the departure of his first-choice goalkeeper ahead of his debut campaign in the Italian top flight.
Chelsea will continue to monitor the situation closely as they weigh up an official opening bid for the French international over the coming weeks.
Failing to secure a world-class presence in goal could undermine the ambitious rebuilding plans currently being implemented by the Stamford Bridge hierarchy.