He has made over 100 appearances for the Naples-based club following a move from Bayern Munich in 2015.
Reina is, however, only under contract until the summer and Milan are ready to make a move to snap up the 35-year-old Spain international as a free agent.
Sporting director Massimiliano Mirabelli told Sky Sport Italia: “We did inform Napoli that we want to speak to Pepe Reina’s agent, because we want to see if there’s a possibility of bringing the player to Milan.”
The World Cup winner is of interest to the Rossoneri as they continue to fend off reports of unrest surrounding current No. 1 Donnarumma.
The 19-year-old committed to a four-year contract at the San Siro in the summer of 2017, but it has been suggested that he remains keen to move on and is being monitored by leading sides across Europe.
Losing a highly-rated academy graduate would deal a major blow to Milan’s future plans.
They have been rejuvenated under the guidance of Gennaro Gattuso, with stability being restored to a team that has endured a rather humbling fall from grace.
Donnarumma is considered to be a key component in a rebuilding process, as is a man currently at the helm on a short-term contract.
Gattuso has restored pride to a side he represented with distinction in his playing days, and Milan are planning to tie him down long-term.
Mirabelli added: “We are always looking to the future. You all know that if I am here, then Gattuso will remain at Milan. He may well remain even without me!”