Hazard, who won the Silver Ball with Belgium at the recent 2018 FIFA World Cup has been strongly linked with a move to Real - as the replacement for Cristiano Ronaldo.
With the Blues facing a season without UEFA Champions League football, it was believed Hazard would look to secure a transfer to Los Blancos.
However, Sarri, who succeeded Antonio Conte at the London based side, has spoken of his desire to work with the Belgian ace within the coming season.
"Hazard is a very high-level player and I think one of the top two or three European players," Sarri told reporters at the official press conference.
"I hope that I will manage to improve him. This is very difficult given he has reached a very high level."
One of Sarri's major achievements at his former side was the conversion of winger Dries Mertens to a centre-forward, who went on to score 56 goals in two seasons under his management.
"With Mertens it's different. Dries had always been an external striker. Everybody thinks that by necessity he reached a very high level.
"But we are talking about two very high-level players. Dries started from lower level. I hope I will improve Hazard too but this is difficult."