The 28-year-old Ecuador international spent one season at Milan following his move from Brighton last summer, managing just one goal and one assist in 19 Serie A appearances after struggling to nail down a regular starting spot.
Transfer expert Fabrizio Romano confirmed on Friday that personal terms had been agreed between player and club, with journalist Ben Jacobs reporting that Villa are now in advanced talks with Milan over a transfer fee, though the exact figure being discussed has not been made public.
Digne, meanwhile, is understood to be close to a move to Paris Saint-Germain, a departure that has left Villa needing fresh options at left-back this summer.
Estupinan previously played under Emery at Villarreal, a relationship the Villa boss is hoping will help smooth the defender's return to English football after three seasons at Brighton, where he scored five goals and provided 12 assists in 104 competitive appearances.
Estupinan is contracted to Milan until the summer of 2030. The defender was part of Ecuador's World Cup squad this summer, making two appearances at the tournament as his country were eliminated before the semi-final stage.
Aston Villa have been busy in the transfer market this window and see left-back as one of the final pieces of business they need to complete before the new season, with Estupinan viewed as an ideal like-for-like replacement for Digne's attacking threat down the left flank.
AC Milan are said to be holding out for a fee closer to their original valuation, having paid around €18m to sign Estupinan from Brighton only a year ago, while Villa have so far been working with a lower figure as they try to find a compromise. The Rossoneri are understood to be willing to sanction the sale as new manager Ruben Amorim looks to reshape his defensive options, having judged Estupinan surplus to his immediate plans.
Should the move go through, Estupinan would give Emery a second recognised option at left-back alongside Ian Maatsen as Villa prepare for another season that will include Champions League football.