Any speculation over the Spanish striker's future will be most unwelcome at Stamford Bridge, with boss Conte's own future with the club seemingly up in the air.
Chelsea's medical team have performed a number of tests on the 25-year-old, but have not got to the bottom of the problem - leaving under-fire manager Antonio Conte unsure on when he will next be able to call upon the former Real Madrid man.
His return to fitness has been affected by the death of a friend and he was allowed time off to return to Spain.
"Obviously I have to respect Chelsea, who made a huge effort to sign me and I'm very happy here, but Madrid will always be Madrid for me".
When pressed about Morata and his season so far, Hazard told Spanish paper Marca: "Yes, he's very happy".
"But Real Madrid are Real Madrid always".
The absence of Morata coincides with Michy Batshuayi's move to Borussia Dortmund on loan, a decision that Conte downplayed.
"Now I think this is not important to say, 'We could have done this' or 'We should have done that'".
Without his pace and composure at the back, Chelsea conceded seven goals in two games against Bournemouth and Watford.
Morata will almost certainly miss Monday's match against West Brom, and has set his sights on a return against Hull City in the FA Cup on February 16. 'He is an important player and he is having a fantastic season'. "I'm not thinking for one moment about the possibility of going away from this club", he said. I repeat: my commitment is totally for this club, like that of my players'.