The German centre-back has fallen out of favour at the Blues and is looking for a move.
Milan want him on loan for the rest of this season, per Sky Sports.
PSG and Tottenham also want the 27-year-old.
Rudiger has two years left on his Chelsea deal, and the Blues hope to extend it by one year before agreeing to a loan move.
They are doing so to protect his transfer value, which would plummet if he only had a year left on his contract next summer.