The Italian thinks Morata, who he worked with at Juventus, is the perfect replacement for Diego Costa if the Chelsea star decides to move to China in the summer.
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But Arsenal have always been closely linked with the 24-year-old Spaniard, who is rumoured to be growing frustrated with an unsettled life in Madrid.
The Daily Telegraph claim Morata has now decided his future is away from the Spanish capital and has gone so far as to inform his close friends that he expects to join Chelsea at the end of the season.
It is believed Morata is also a huge fan of Conte and is keen to reunite with the manager following their time together in Serie A.
Morata, who has netted 12 goals in 31 appearances in all competitions this term and is valued at around £43million by Real Madrid.
Morata returned to Real Madrid this summer, leaving Juventus, with a strong intent to displace Karim Benzema as the first choice striker, but he has failed to gain the necessary trust from Zinedine Zidane and as a result remains the firm second-choice.
Although he returned to Madrid by becoming a more rounded and mature player, with the vast experience of a different style of football and the reward of a first full Spain cap shortly after his switch to Turin.