Willian, 29, cut a forlorn figure at times under Conte and has been linked with Manchester United, Barcelona and Real Madrid.
Hazard was one of the stars in Russian Federation this summer, scoring three goals and helping Belgium to a third-placed finish - their best ever World Cup performance.
"I'm very happy", Sarri said. It was a very positive conversation. "I am happy about it".
Carlo Cudicini, another former Chelsea goalkeeper, remains as assistant to Sarri.
Maurizio Sarri, though, has come out to give yet another update to the situation, as Real Madrid are regularly linked to the Belgium worldwide.
"Chelsea is a big club". 'I don't know in the future. 'It depends especially on him I think.
"I think David will be very important for the team, to support me".
He said: "We are not at the top level now".
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As well as Hazard, Thibaut Courtois could be off to Spain as doubts grow regarding his future.
Sarri was quick to point out that City are considerably further ahead in their tactical development under Guardiola, yet he will still try to attack the Premier League champions today. Under Sarri's guidance at Napoli, the Brazil-born midfielder had blossomed into one of Europe's most coveted players, and had risen to such heights in Italy that he was even anointed as the heir to the great Andrea Pirlo. "But we have it all to start well in the league".
"I have to win, and then it depends on the club, but I want to stay here for a long time". At this moment of the season it is no more important.
"We have to improve, of course".
Bournemouth will be hoping to wrap up the signing of Colombian defensive midfielder Jefferson Lerma for a club-record fee.
Maurizio Sarri is "very confident" Willian will remain at Chelsea and insists there is no problem with the Brazilian after he returned late from his holiday.
Cesc Fabregas may miss out due to a minor knee problem.