The Spanish transfer window is yet to shut, with around two weeks remaining when it will close at the end of August.
Picking up 10 yellow cards last season, the second most in the Premier League, the Swiss global grabbed his customary booking before being dragged off at half-time.
Speaking after the win, Hazard said: "Everybody knows what I have said after the World Cup".
But he has now pledged his commitment to Chelsea for the foreseeable future.
But the 25-year-old Spain worldwide, who was left out of the country's World Cup squad, was on target in Chelsea's 3-2 win over London rivals Arsenal in Premier League action on Saturday. I think the result is 3-2 but we also think we did [have] chances to score more.
Speaking to Chelsea TV, Morata said that he struggled during last season because of the way he was asked to play under former Blues boss Antonio Conte. A lot of it nonsense.More news: "I won’t go" - Eden Hazard confirms Chelsea stay
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"First of all I'm happy about the win and that's the most important thing", he said after the game.
The Daily Mail say that Danny Drinkwater is to be used sparingly under Sarri, featuring in the League Cup or Europa League only this season - but the club are hoping that a loan-offer can materialise.
"I am looking forward to buying a house and I can't wait for the babies to grow up to put them into school".
The 27-year-old has been a vital part of Chelsea's team since his arrival at the club from LOSC Lille in 2012. "And then today I think the team competed well, had chances in the match, and also the young players are playing each match and they are growing up with us". I'm good where I am now. "We'll see what happens in a year or two years". Inside there were 15 terrible minutes.
Sarri admitted his side's defensive display as they surrendered a 2-0 lead was "horrible", as the Italian offered up this honest assessment of a insane game.
The club who wanted me and the coach that believes in me.