The Blues have been credited with a strong interest despite already landing Michy Batshuayi, and Express Sport understands Antonio Conte is lining up a third bid worth £67million for the Spanish striker.
Arsenal have also been tracking the striker, with Arsene Wenger keen to beef up his attack.
Though Real activated his £23m buy-back clause, Premier League suitors haven’t been put off.
But the 23-year-old is delighted he is able to resume his career at the Bernabeu.
Speaking earlier this week during Real’s pre-season tour of Canada, Morata told the club’s official website: “It is incredible to be here again.
“It is a dream come true and I can’t wait to get started.
“I can’t wait for tomorrow to arrive so we can get to work.
“Zidane works hard and does a lot of physical work. I have had two great years at Juventus, I learned a lot and I can only be thankful because without this experience I would not be here.”