Kessie has recently been linked with Man United as well as other premier league clubs.
Kessie whose contract is expected to expire by 2022 has been instrumental for AC Milan of recent.
According to Mundo Deportivo Barcelona are targeting Kessie with the possibility of signing him for free in the summer of 2022.
Barcelona with little financial power will hope to bring the 24-year-old to Camp Nou for a free transfer.
Kessie has been one of the most important players to Milan’s high pressing system and has become Stefano Pioli favorite.