Chelsea manager Antonio Conte faces a battle to keep hold of the winger, who returned from an impressive loan spell with his old club Juventus
The former Fiorentina winger is well known in Italy and had a successful loan spell at Juventus last season, but he is in contention to start against AC Milan in his club's International Champions Cup match Wednesday.
The 28-year-old faces stiff competition for places in his position at Chelsea, having to compete with Willian, who won Player of the Year, Pedro and Eden Hazard, with Conte acknowledging that he is a player who is drawing interest.
"Juan Cuadrado is a Chelsea player as I said with Diego Costa," Conte said. "He has worked very hard and is training very hard with us. Everyone knows what I think about him and everyone knows that good players have a lot interest in a transfer window."
"Now he is a Chelsea player and happy. If you will ask me what could happen in future I couldn’t answer about Juan Cuadrado nor other players."
Conte has long been an admirer of the Colombia international since his spell as the manager of Juventus but lost out on signing him to Chelsea due to his old club's poor relationship with Fiorentina.
Milan face competition from Cuadrado's old club Juventus, who wanted to make their loan permanent last season after their domestic double-winning season, before Conte blocked the deal.
Rossoneri head coach Vincenzo Montella refused to be drawn on whether he was interested in bringing Cuadrado to the San Siro. When questioned, he said: "He is a Chelsea player — you will have to ask him."