The Belgium striker had been linked with a move to Real Madrid and in July the 27-year-old said it “might be time for something different”.
Hazard’s Belgium and former Chelsea team-mate Thibaut Courtois joined Real on transfer deadline day on a six-year deal.
“Hazard is with us. It’s not a problem,” said Sarri.
“I have spoken with him three, four times, for everything. He never said anything about the market. He’s very happy to stay here.
“Here the market is closed, so we cannot change important players now. It’s impossible.”
Hazard, who scored three goals at the World Cup in Russia – including Belgium’s second against England in the third-place play-off – has two years left on his contract at Chelsea.
Since moving to Stamford Bridge from French club Lille for a reported £32m in June 2012, Hazard has helped Chelsea win two Premier League titles, the FA Cup, League Cup and Europa League.
In June Hazard said he would “listen” if Real offered him a deal, but added he could stay at Chelsea for “many years”.
Sarri said he feels his squad is complete after the signings of goalkeeper Kepa Arrizabalagaand midfielder Mateo Kovacic in the build-up to the transfer deadline.
The Blues triggered Kepa’s release clause of £71m to sign him from Athletic Bilbao, while Kovacic came in on a season-long loan from Real.
“We lost maybe one of the most important goalkeepers in the world now but we bought a young goalkeeper, I think one of the most important amongst the young goalkeepers in Europe.”