The Italian side have offered a €25m fixed fee and €5m in add-ons to reach €30m, per Fabrizio Romano.
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It is believed Chalobah is keen on making the switch to the Serie A and for a new challenge to play under manager Cesc Fabregas.
The 27-year-old made 34 appearances for The Blues last season, scoring three goals.
With the arrival of Maxence Lacroix from Crystal Palace in a deal worth £52 million, it might prove to be the right time for Chalobah to leave Stamford Bridge this summer.