Reports suggest the Spain Under-21 international is on the verge of a switch to the Italian champions, having been linked with an exit from the Santiago Bernabeu in recent months.
Morata has struggled for a regular spot under Carlo Ancelotti due partly to the presence of star names such as Cristiano Ronaldo, Gareth Bale and Karim Benzema.
And the 21-year-old's move appears close to completion, as he told Marca: "I'm very happy. This is a new challenge for me."
The Real youth product won the Copa del Rey twice as well lifting the Liga title at the club - with reported interest from clubs around Europe following.
Arsenal, Wolfsburg and Villarreal were all apparently targeting the Spaniard but instead he looks set to link up with Antonio Conte at Juve.
Should the deal go through, he will likely compete with Carlos Tevez and Fernando Llorente for a starting berth in Turin.
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