Both teams are already thought to be making preliminary plans for the summer transfer window and strengthening their respective attacks remains high on their list of priorities.
The London outfits attempted to bring Morata to England last summer but after Real Madrid activated their buy-back clause with Juventus, the Spaniard returned to the Bernabeu.
Alvaro Morata is attracting interest from Chelsea and Arsenal
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Reports in Spain suggest the 24-year-old is unhappy in the capital though, and The Telegraph claim he prefers a move to Chelsea over Arsenal.
They claim Morata has already told friends he expects to move to Stamford Bridge at the end of the campaign.
The 24-year-old is a big fan of Conte’s work and the Italian boss helped set up his move to Juve back in 2014 before he left to coach Italy.
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Antonio Conte is looking to bolster his attack with the signing of Alvaro Morata
Alvaro Morata has reportedly told friends he expects to move to Chelsea
But the Spain international won’t be available on the cheap with Real reluctant to listen to any offers below £50m.
Morata, who is under contract with Real until 2021, has netted 10 goals in all competitions for the La Liga giants this season.