The 25-year-old was omitted from Julen Lopetegui's Spain World Cup squad, and has struggled to find his form at Stamford Bridge for the Premier League outfit this season.
The culmination of his season saw Olivier Giroud start in the FA Cup final against Manchester United instead, and cemented what has been a disappointing season for the Spaniard.
Although Juventus have reportedly expressed an interest in taking back their striker, AC Milan are also considering a move for Morata, depending on his market value.
Chelsea are also steeling themselves for offers from top-tier clubs for several of their star players including Eden Hazard, Thibaut Courtois and Willian.