The Spaniard has failed to establish a starring role under Zinedine Zidane this season with Karim Benzema, Cristiano Ronaldo and Gareth Bale leading the line.
Antonio Conte is a big fan of the forward having signed him during his spell at Juventus and the Italian is said to be keen to bring him to Stamford Bridge.
Alvaro Morata is reportedly keen on a move to Chelsea Real Madrid transfer odds: Which Premier League aces could move? Thu, March 30, 2017
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Morata recently added fuel to the fire by declaring he expects to link up with Conte sometime soon.
The report states Conte has already promised him regular game time under his leadership as well as trophies.
Diario Gol suggest Morata is already putting the wheels in motion over a move to London with his girlfriend buying a house in London.
Antonio Conte is hoping to link up with Alvaro Morata at Chelsea Chelsea line-up predicted to face Manchester United Wed, April 12, 2017
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Despite a move to England’s capital being on the cards, Chelsea will have to stump up a big fee for his services.
Madrid chief Florentino Perez will reportedly not entertain offers less than £34m.
Morata, who has netted 11 times in La Liga this season, is under contract with Madrid until 2021.