Kessie has started just six La Liga matches under Xavi in his first year at Barcelona this season, as the Catalonian club sealed the league title.
The Ivorian enjoyed five fruitful seasons at Inter's bitter rivals Milan, but he would not be the first man to represent both clubs.
Journalist Gerard Romero claims that the Nerazzurri are interested in the 26-year-old, and are monitoring his situation at Camp Nou.
Kessie could follow the likes of Ronaldo, Roberto Baggio, Zlatan Ibrahimovic and more recently Hakan Calhanoglu in representing both sides of the divide.
It is believed around €25-30m (£22-26m) will be enough to secure Kessie's services, as the midfielder has struggled for regular game time behind Pedri, Gavi and Frenkie de Jong at Barca.
With Ilkay Gundogan also being strongly linked with the club, that would potentially see Kessie fall even further down the pecking order, leading to a possible exit.