Milan are reportedly still a long way off agreeing terms with Lille for Renato Sanchez, but hope to meet them halfway at €15m.
The Portugal international has long chosen the Rossoneri as his next destination and agreed personal terms, rejecting all other proposals.
However, the Ligue 1 club are proving less simple to convince and Sky Sport Italia report they turned down the latest offer of €10m.
The asking price is €20m, so it is hoped they will eventually settle and reach an agreement for circa €14-15m.
Sanches turns 25 in August and his contract with LOSC is due to expire in June 2023.
Lille paid €20m plus bonuses to sign him from Bayern Munich in the summer of 2019.
This season, the midfielder played 32 competitive games for LOSC, scoring two goals and providing five assists.
All parties remain confident a deal will be done eventually, but Milan are still trying to keep their purse-strings tight, even after the takeover from American investors RedBird.