And Spanish media outlet Diario Gol claim the forward will leave Madrid this summer, with Chelsea his No1 option.
Morata added fuel to the flames this week by declaring he expects to link up with Conte soon.
According to the report, Conte has already promised him regular game time at Stamford Bridge in addition to regularly challenging for trophies.
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And it is also claimed his girlfriend, Alice Campello, has already set the wheels in motion to purchasing their first property in London with a number of house viewings.
Despite the star being in favour of a move to the capital, Chelsea will have to cough up a significant fee for the star.
Alvaro Morata has told Real Madrid chiefs he is leaving this summerEPAChelsea boss Antonio Conte is leading the chase for Real Madrid forward Alvaro MorataRex FeaturesAlvaro Morata has bagged 11 goals for Real Madrid this seasonReuters
Madrid president, claim the reports, will not accept anything less than £34million for the attacker.
Morata has scored 11 times for the La Liga leaders this season.
He is under contract until 2021 with the Los Blancos.
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