Diario Gol says Morata is ready to call time on his Chelsea career if Conte is relieved of his duties.
The Spaniard is said to feel important under the Italian and would be devastated if he left.
Speaking after his summer arrival, the 25-year-old said: “I came to Chelsea because one club and one coach believed in me.
“Now I have all of these things and I'm very happy."
Morata fears his importance at Chelsea will lessen if Conte is axed.
And he is also supposedly unhappy at the club's plans to replace him with Luis Enrique.