The 24-year-old midfielder started 36 times in the Rossoneri’s successful Serie A campaign last time out, playing a crucial part in the club’s second-placed finish.
However, the Serie A outfit may be forced to sell the Ivorian this summer due to financial concerns arising from the coronavirus pandemic.
La Gazzetta dello Sport claims that the 18-time Italian champions are confident that they can still land £42m for the Ivory Coast international, whose contract will expire next summer.
The Gunners are said to lead the way for Kessie’s signature.
Kessie has spent four years at San Siro.