The Reds are now ready to follow up with a firm bid for the Ivorian.
The 24-year-old has just one year remaining on his current deal with the Rossoneri and talks over an extension are said to be at an impasse.
The battle for his signature will be tough, with Milan set to offer a £5m salary in order to try and keep the Serie A star in Italy.
Kessie bagged 13 goals (11 on them penalties) and four assists over the course of the last campaign, his best return since arriving at the San Siro in 2015.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!