Kessie has also been linked with Everton and Arsenal in recent weeks.
The 23-year-old has become one of Milan’s key performers in the past two seasons, with the San Siro side securing him on a permanent contract from Atalanta in the summer after two years on loan.
Italian website Tutto Mercato Web claim that Newcastle have contacted AC Milan over a possible transfer, but their valuation of the Ivory Coast international falls way short of the mark.
Having just secured Kessie on a permanent deal, the Toon’s feeble offer of a €5m loan deal with an option to buy is likely to be dismissed sharpish.
The Rossoneri seem in no rush to see the Ivorian leave Milan any time soon, having paid €24m for him last summer – any fee from Newcastle to prise him away from Serie A would need to be significantly weightier.