Arsenal are also said to be still interested in the forward.
Spain's Alvaro Morata reacts
Real Madrid exorcised a buy back clause for the Spaniard to return to the Bernabeu for £23 million following a successful two seasons in Serie A - but it hasn't stopped any speculation from being generated surrounding his future.
Italy's Marco Parolo fouls Spain's Alvaro Morata
The Mirror's report also states that Arsenal retain an interest in the 23-year-old and that Juventus could have demanded around £45 million for him if Madrid had not returned for him.
Morata's agent has said the player has had offers from the Premier League, with the player saying at the weekend: “I do not have to prove anything to anyone. I am a player of Real Madrid and they will decide if they want me. Otherwise we will find another solution.”
Italy head coach Antonio Conte
It seems that both clubs are intent on signing a striker this summer but it would represent something of a merry go round for Morata if he were to move - who scored three goals during Spain's Euro 2016 campaign which came to a conclusion against Antonio Conte's Italy yesterday.
The move back to Real Madrid may have made things harder for Chelsea and Arsenal to land Morata, and if there is any indication that he could get regular game time at the Bernabeu next season, he may opt to stay in Spain ahead of the coming season.
Spain's Alvaro Morata shoots