Real Madrid have just exercised a £25million buyback option on the Spain international, who has scored three goals in three appearances so far at the European Championship.
However, Los Blancos are planning to sell on the former Juventus striker this summer for £40million rather than keep him on the books at the Bernabeu.
According to The Telegraph, Chelsea have already opened talks with the La Liga giants to wrap up a west London swoop for the 23-year-old.
Incoming manager Antonio Conte is a known admirer of Morata’s, having played a role in his 2014 move to Juventus before stepping down as Old Lady boss during the same summer.
But Chelsea’s negotiations with Real Madrid follow a scouting mission from owner Roman Abramovich, who watched the Spain assassin score against Croatia on Tuesday.