The English transfer window closed at 5pm on Thursday, but other clubs from Europe's top leagues can still sign players until the end of the month, including from Premier League teams.
Willian has been linked with a move to Barcelona, while Hazard has also been tipped to join Real Madrid, with compatriot and former Chelsea teammate Thibaut Courtois recently urging him to join Los Blancos having made the same move himself this summer.
However, Sarri has ruled out the possibility of any more high-profile exits and expects Hazard to sign a new contract at Stamford Bridge, with his current deal expiring in 2020.
"I think it's impossible. Here the market is closed, so we cannot change important players now. It's impossible," Sarri told reporters when asked about the duo's futures.
"Hazard is with us. I think definitely. It's not a problem. I have spoken with him three, four times, for everything. He never said something about the market. I think he's very happy to stay here.
"I don't want to discuss about contracts. It's not my job. My job is on the pitch. My job is to improve the players. My job is to try to win matches. It's not to sign new contracts. I have seen a player very happy to stay here. So I think it will not be a problem, the new contract."
Chelsea's first match of the new Premier League season comes away to Huddersfield Town on Saturday.