Manager Antonio Conte has come under major pressure after battling with the Chelsea board over transfer policy while losing three of their last four games.
Top scorer Morata, who has 12 goals this season, has missed Chelsea’s last five games with a back injury that is worrying the club because it is not responding to treatment as quickly as had been expected.
Before that the Spaniard, bought from Real Madrid in the summer as the club’s marquee signing, had scored only twice in his previous 11 games in an equally worrying dip in form.
Conte, whose side face bottom club West Brom in a must-win game at Stamford Bridge on Monday, said: “Morata will not be ready.
“If you ask me whether he needs a day, a month or the rest of the season, I don’t know. I’m worried.
“He is a very important for us but has been missing for a long period of time. I don’t know how long he will be out. We are struggling a lot to find a solution to solve the pain in his back.”
New £18m signing Olivier Giroud is now expected to make his full debut against West Brom, while defender Andreas Christensen could also return.
Conte, who has insisted he intends to see out the final year of his contract, gave his players three days off but when they reported back told them that they had to “be men, not kids”.