The Turkey international was linked an exit from the San Siro with his contract set to expire in the summer.
Manchester United have been heavily linked with the exciting playmaker.
But according to CalcioMercato, the 26-year-old is thinking about lowering his contract demands to remain with Milan.
Calhanoglu has played an important role in Milan's terrific start to the season, which sees them sit on top after nine games.
His representatives will arrive in Milan in the next fortnight to continue negotiations with the Serie A giants.