Chelsea have already had offers of £50m and £62m turned down by Real but new manager Antonio Conte is a massive fan of the 23-year-old and is determined to get his man.
Real activated the £23.5m release clause in Morata’s contract with Juventus this summer to bring him back to the Bernabeu, with the intention of making a quick sell-on profit, with Chelsea always keen.
Conte said: “We know our targets and the important thing is that between me and the club there is a great synergy on the transfer market.”
If a deal cannot be worked out with Real, Chelsea could turn to Everton’s Romelu Lukaku, in whom interest has been reactivated.
But the Stamford Bridge hierarchy still believe that the Belgian is vastly over-priced at £65m – especially as they sold him to Everton for only £28m two years ago.
Chelsea have enquired but the French club want about £67m for the 29-year-old Uruguayan, who has turned down a new deal.
Chelsea defender Kurt Zouma, meanwhile, hopes to be available for selection in two months after having surgery on a knee injury he suffered in February.
The 21-year-old, who returned to training on Monday, suffered a knee ligament injury in the 1-1 Premier League draw against Manchester United in February and missed the rest of the season.
“I’ve been working alone for a while and now I’m training, learning and improving with the guys. I didn’t know I would be back on the training pitch by now, I thought it would be a bit later,” said Zouma.
“My knee is OK and I don’t have any pain, which is great. I’m not fit enough yet but hopefully in six weeks or a couple of months I will be, we will have to wait and see.”