The flying winger arrived at Stamford Bridge for £26.1m back in February 2015 but has managed just four Premier League starts since his arrival.
He was sent out on loan to Juventus for the whole of last season and the former Fiorentina man impressed back in Serie A, scoring four goals in 28 league appearances for the eventual champions.
Juve have been strongly linked with a permanent move for the 28-year-old this summer but now it has been reported that AC Milan have joined the chase.
According to Il Milanista, the Rossoneri will approach Chelsea about a season-long loan deal with a purchase agreement in place for next July.
Alternatively, Milan may opt to buy him outright this month using the funds they would glean from selling Carlos Bacca to West Ham.