Sky Sports Italy correspondent Gianluca Di Marzio has reported on his personal website that contact has been made about a potential deal that could see the 24-year-old move to Stamford Bridge next season.
The report claims that the Premier League champions believe the Spaniard is the perfect candidate to lead the line for Blues next season after top summer target Lukaku looks set to complete a deal to league rivals Manchester United.
This comes after the Manchester club announced on their official Twitter account that they had agreed a fee to sign the Belgian striker from Everton.
Morata has been heavily linked with a move to Old Trafford throughout the summer but the Lukaku deal indicates that the potential transfer is off the table, which could open the door for Chelsea.
Chelsea boss Antonio Conte is facing a crisis at the club regarding strikers as the Telegraph recently reported that talisman Diego Costa has already said goodbye to his teammates after being informed that he was no longer required at the West London club.
Morata is certainly a player who can deliver the goods for the Blues as he contributed with 20 goals in all competitions for the La Liga champions last season.
The Spaniard currently has four years remaining on his contract at the Bernabeu.