The Belgian has long been on Madrid's radar as Julen Lopetegui considers finding a replacement for Cristiano Ronaldo, who left for Juventus earlier in the summer transfer window.
Thibaut Courtois has already made the move from Stamford Bridge to Spain, and has insisted that it would be "fantastic" if Hazard were to join him in Madrid.
Goal understands that a contract offer is on the table for Hazard - a figure of around £300k-a-week that would make him the highest-paid player in the club's history - but he is not close to signing the new deal.
Sarri, though, is adamant that his star man wants to remain at the club, revealing that, given he wouldn't be able to sign a replacement now the Premier League window is closed, it's "impossible" Hazard will be leaving.
He told reporters: "I think it's impossible. It's impossible because, here, the market is closed. We cannot change important players now, so I think it's impossible.
"Hazard is with us. I have spoken with him three or four times for everything, and he never said something about the market. So I think he is very happy to stay here.
When asked about a new deal for Hazard, Sarri added: “I don't want to discuss about contracts. It's not my job. My job is on the pitch, to improve my players.
"My job is to try to win matches. It's not to sign new contracts. But I have seen a player who is very happy to stay here, so I think it will be no problem, the new contract."
Regarding Courtois's departure, Sarri suggested there were "personal reasons" involved in the goalkeeper's decision to leave and that, following the arrivals of Mateo Kovacic and Kepa Arrizabalaga, his squad is "complete".
He added: "I am very happy. Courtois' situation was clear, he wanted to go to Madrid. There were some personal reasons. I don't know really.
"But we bought a young goalkeeper, one of the most important in Europe. I am really happy. And to Kovacic, because he has the characteristics for us. The squad is complete."