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The Turkey international has reached an agreement in principle over a three-year deal with the Serie A champion, according to Sky Sport Italia.
The deal is said to be worth more than the offer from Milan, who had hoped to see him extend his contract, which expires next week.
Speaking to TRT Spor on Monday before his return to Italy, Calhanoglu said: "I've reached an agreement with Inter. I will sign the contract tomorrow."
Calhanoglu made 172 appearances for Milan following a 2017 move from Bayer Leverkusen.
He played in all three of Turkey's Euro 2020 group games as it lost to Italy, Wales and Switzerland.
Calhanoglu scored 32 goals and provided 42 assists for Milan in all competitions, averaging one direct goal involvement in a little over every two games.
Last season, he created 98 chances in Serie A, the highest number of any player in Europe's top five leagues. Inter's top chance-creator in the league in 2020-2021 was Romelu Lukaku, with 52.
Among players in Italy's top tier, only Rodrigo De Paul (10.27) had a higher expected assists figure than Calhanoglu (8.47), despite the Milan man having made three fewer appearances.
He is one of just four Turkish players to reach 50 goals in the top five European leagues since the turn of the 21st century, after Mevlut Erdinc (92), Nihat Kahveci (76) and Halil Altintop (67).