The Ivory Coast international started 36 times in Milan's successful Serie A campaign last time out, playing a big part in the Rossoneri's second-placed finish.
However, the Italian side may be forced to sell Kessie this summer due to financial concerns.
La Gazzetta dello Sport claims that Milan are confident that they can still land £42m for the 24-year-old, despite only having 12 months to run on his deal.
Arsenal are said to lead the way for Kessie's signature, two years after first showing an interest in the central midfielder.
Kessie, who has spent four years at San Siro, was recently named in Sports Mole's Serie A Team of the Season for 2020-21. body check tags ::