The Spaniard has not been included in his team's squad for their last four Premier League games, with that streak set to continue against Crystal Palace on Sunday.
Hazard has been deployed as a centre-forward in the absence of a more reliable option, and has scored three times in those four appearances.
Sarri has been so encouraged by the Belgian's displays that he feels he is starting to mirror Morata's best attributes - casting doubt over the Spaniard's long-term prospects.
The Italian said: “We need to be balanced on the pitch and be more solid.
"In the last matches I prefer this solution (Hazard at forward). For the future everything is open.
“I think that Alvaro is better in the box and better to attack spaces but I have to say Eden is improving as you saw in the last match with the second goal, he attacked very well the space.
“It’s different as Eden is better when he comes to play with the midfielders and opens spaces. He’s another way of playing.
“I want to see the physical condition of the players. We will decide after training.
"Alvaro’s potential is to be a very good player. He’s fit, yes.”
Despite an encouraging start to life at Stamford Bridge, the goals and appearances have dried up for Morata who is facing a January exit.
Twenty-two goals have come in 69 outings for Chelsea in 18 months since he joined from Real Madrid, while AC Milan and Barcelona have been linked with ending this misery in west London.