According to Sky Sport in Italy, the 39-year-old only a few weeks after leaving Real Madrid had constructive conversations with AC Milan.
New sports director Igli Tare now believes that an agreement between all parties is imminent and Modric will be an AC Milan player in the coming days.
The arrival of Modric coincides with the Dutch midfielder Tijani Reijners who are getting closer to Man City with an agreement that would already have been.
The Ballon d'Or winner of 2018 left Real Madrid after 13 years with an incredible 28 trophies under his belt.