Antonio Conte is keen on snapping up the Spanish target man as Diego Costa’s replacement.
The charismatic Italian chief has turned to Morata after Manchester United signed Romelu Lukaku from Everton.
But, according to Spanish news outlet Don Balon, Chelsea could be thwarted again.
It’s suggested ambitious Milan are circling as they look to become a force in European football again.
However, it’s suggested Morata isn’t keen on a move to the Serie A giants.
The 24-year-old spent two years at Juventus and doesn’t want to join their league rivals.
Man Utd target Alvaro Morata and wife Alice Campello enjoy romantic boat trip
Don Balon say Morata’s heart is firmly set on a move to Stamford Bridge.
Morata was re-signed by Real last summer from Juve for £27m having originally left the Bernabeu in 2014.
Conte originally signed him at Juve, although never got to work with him having accepted the Italy national team job shortly afterwards.