There had already been suggestions over the last week that Vlasic was being targeted by the Rossoneri, but the €35m asking price had seemed outside their price range.
According to Calciomercato.com, the talks are progressing and CSKA Moscow would be prepared to accept €28-30m.
Milan hope that the Russians will accept a loan with option to buy or even an obligation, therefore spreading out the cost over several years.
The Corriere dello Sport and some other Russian sources have pointed towards an offer worth €25m, with bonuses and add-ons that could take it towards an agreement.
Vlasic is said to be keen on the idea of joining Milan in Serie A and the Champions League.
His previous clubs include Hajduk Split and Everton, but Vlasic contributed 10 goals and five assists in 21 Russian Premier League appearances this season.
🇭🇷🇮🇹 VLASIC UPDATE:
💰 Milan have submitted a 25 million euro bid
❌ CSKA are holding out for 30
✅ Vlasic is keen on the move and is expected to agree to personal terms
We might reach a conclusion soon! ⏳
— Russian Football News (@RusFootballNews) July 13, 2021