The Belgium international has made a brilliant start to the Premier League season following a return of five goals in five games so far.
Maurizio Sarri has unburdened Hazard of his defensive duties to allow the Belgian star to play with more freedom in the Blues side.
The Italian head coach has started with Morata in a striker role in four of their opening five Premier League fixtures.
The Spain international has only scored one goal in the Premier League so far in a underwhelming start to the English top flight.
Giroud, on the other hand, has made three assists to help the west London side ease to five successive Premier League victories.
The 32-year-old has struck up an understanding with Hazard since his move to Chelsea FC from Arsenal in a £21m deal in the January transfer window.
Former Liverpool FC defender Carragher believes Hazard is an admirer of Giroud and what the Frenchman brings to the Chelsea FC team.
“I think he is saying that [he prefers playing with Giroud],” Carragher told Monday Night Football on Sky Sports.
“You don’t normally hear something like that. No disrespect to Morata but I think he is saying to the manager that he wants to play with this guy more often than not.”
Chelsea FC finished in fifth spot in the Premier League table last term to miss out on a Champions League spot.
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