Antonio Conte worked with Morata for two seasons after the Italian coach took him to Juventus in 2014.
And Spanish daily newspaper AS claim that Conte is desperate to work with the Spain international at Stamford Bridge.
Morata has struggled to break into Real Madrid boss Zinedine Zidane's starting XI this season, instead playing a back-up role to Karim Benzema.
Chelsea are reportedly readying a bid of £56million to sign Alvaro Morata
Antonio Conte worked with Morata for two years during their time at Juventus
The striker has made just nine La Liga starts since joining Madrid last summer but has found the net eight times.
But the report claims the 24-year-old has grown frustrated at a lack of opportunities under Zidane.
And Morata believes he will be given more of a chance under Conte who helped him establish his career in Turin.
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Conte has told Roman Abramovich he wants to sign Morata
The Italian coach wants to make the deal happen and has told Chelsea owner Abramovich to stump up the cash for a summer bid.
Madrid are reportedly asking for £40million and Chelsea are supposedly willing to go as high as £56m to get the transfer over the line.