The 25-year-old midfielder will be out of contract at the end of the season and AC Milan are yet to convince him to sign a new deal.
His contract situation is being tracked by several clubs in Europe who are interested in snapping him up on a free transfer in the summer.
Tottenham have their eyes on him as a long-term target and he has also been linked with a move to Juventus, Barcelona and Paris Saint-Germain.
And according to Italian daily Gazzetta dello Sport, current league leaders and defending Serie A champions Inter also have their eyes on Kessie.
The midfielder’s contract situation has been noted by Inter, who are always alive to the possibility of signing quality free agents.
Last summer they managed to convince Hakan Calhanoglu to cross the Milan divide on a free transfer.
Kessie has emerged as a target and Inter will keep themselves abreast of his situation at the San Siro over the course of the next few months.
For the moment, AC Milan are resigned to seeing him walk away on a free transfer in the summer.
It had been widely suggested that Kessie has a verbal agreement with Barcelona, but that talk appears wide of the mark.
