The Blues announced they had reached an agreement for the striker last night.
And Morata has arrived in Lond on today to undergo his medical and discuss personal terms with the club.
But Spanish outlet Diario Gol say the 24-year-old made sure to give Zidane a piece of his mind before departing the Bernabeu.
Morata was unhappy with being down the pecking order when he felt his performances merited more starts.
The reports say the striker feels betrayed as Karim Benzema was picked ahead of him because of his friendship with the manager.
Morata’s agent Juanma Lopez was the man who delivered the message on his client’s behalf.
Similar situations were faced by Lucas Vazquez, Marco Asensio, James Rodriguez and Isco last season.
Isco did manage to force himself into the Real side following injury to Gareth Bale.
But Rodriguez has since moved to Bayern Munich on a two-year loan deal with the view to a permanent switch to the Bundesliga.
Morata will look to impress at Chelsea as he leads the line for Antonio Conte’s side.
The Spaniard is expected to replace Diego Costa who has been told he is surplus to requirements at Stamford Bridge.