The 25-year-old defender completed a move to Chelsea from Italian club Torino on transfer deadline day to help bolster Antonio Conte’s defence.
Zappacosta has established himself as one of Serie A’s most-productive full-backs during a three-season stint at Torino.
The Italy international came up against Chelsea striker Morata during his spell at Torino as the Spanish forward played for Torino’s bitter rivals Juventus.
Morata completed a move to the Premier League champions in a £58m deal from La Liga giants Real Madrid in the summer transfer window following his return to the Spanish capital last summer.
And new Chelsea signing Zappacosta revealed that he doesn’t have fond memories of coming up against his new team-mate during their time together in Serie A.
“I don’t have very good memories because when I played against him in the Turin derby, Morata scored two goals for Juventus and we lost the game,” Zappacosta told Chelsea’s website.
Morata opened his Premier League account with a consolation goal in a 3-2 loss to Burnley on the opening day of the Premier League season.
The 24-year-old has also scored in Chelsea’s 2-0 victory over Everton in their last Premier League outing before the international break.
Chelsea will return to Premier League action with a trip to 2016 champions Leicester City on Saturday 9 September.
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