Hakan Calhanoglu s agent has held positive talks with Milan over a new contract for the midfielder.
The Turkey international s deal expires at the end of the season and there has been speculation Manchester United are interested in a free transfer.
United could strike a pre-contract agreement with Calhanoglu as early as next month, but it appears the player is increasingly likely to stay with the Serie A leaders.
His agent, Gordon Stipic, met with Milan directors on Wednesday and is optimistic an extension can be agreed.
There are suggestions both parties are eager to tie up negotiations quickly due to the looming prospect of stricter coronavirus regulations in Italy, which could make talks more difficult.
It was a positive meeting, Stipic told TUTTOmercatoWEB.
We re in the negotiation phase. We ll see. We re working on it and we ll meet again.
We ll keep in constant contact for future appointments with Milan s directors.
Calhanoglu has created 43 goalscoring chances in 11 league games this season, at least 13 more than any other player in Serie A.
In July, he became the first Milan midfielder since Kaka in 2008 to be directly involved in at least one goal in five consecutive matches.
Milan, who are unbeaten in the league this season and three points clear of Inter at the top of the table, face Genoa on Wednesday.