The Blues secured the future of another one of their key men yesterday when Cesar Azpilicueta committed his future until 2022.
Sarri wants “important” duo David Luiz and Cesc Fabregas – both out of contract next summer – to stay too.
But Belgian talisman Hazard will be the big one if Chelsea can reach an agreement – and they are ready to make him their £300,000-per-week top earner.
Hazard, 27, has kept his cards close to his chest, admitting long-time admirers Real Madrid are his dream club, but at the same time, he could easily retire at Chelsea.
“You know very well that Eden is very important for us, like every special player. He’s important for his club,” Sarri said.
“It’s up to him. The club is available to sign a new contract immediately, but it’s up to him if he wants to renew or not.
“I want Eden here, of course, but I want him here if he wants to stay here.”
Sarri believes Luiz and Fabregas are among Chelsea’s new leaders.
But with the club’s policy of only handing one-year deals to players over 30 he added: “The club wants a short contract, and the players want a long contract, so it’s difficult.”
A busy period for Chelsea of games every few days between now and the start of January continues tonight at Wolves, who have been preparing foer the visit of Hazard and Co by mimicking the Belgian playmaker in training.
“Even the players that are not playing realise how important they are to prepare for a game like this,” said manager Nuno Espirito Santo.
“They work themselves and transform themselves into Hazards to create situations. This is what you want from a squad. Everybody working.
“I’ve had ‘Hazards’ doing one versus ones and this is the way we work. Chelsea have a lot of quality but Eden Hazard is exceptional. He’s up at the top of Premier League players.
“But also Chelsea are also one the top of the teams in the division and that’s what we have to look at.”
Just one point from the last 18 available in a six-match winless streak is hardly encouraging, and star player Ruben Neves is suspended just to make matters worse.
“I’m sleeping okay, but not as well as before, of course,” said Nuno. “Of course it affects me. It affects everybody, but you have to face it.
“You have to be ready for anything and everything and accept everything the way things are.”
Nuno is drumming into his players to remember just how good they were at the start of the season and not get disheartened by a worrying run.
He added: “The core of the squad is the same that played so well all last season and when we started fantastically at the beginning of this season.
“We had really good performances. We have to analyse what happened in this moment and remember there is a long, long way to go.”
He wants to recall the blistering form which made Wolves the talk of the town, adding: “The truth is we’ve had fantastic moments so that now we are in a bad moment it still gives us something to hold onto.
“We must solve it. It’s a building process. Some people might call me crazy but this is what I believe and this is how we work.
“I believe we are going to come stronger. The fans will be massive to us. Everybody knows the impact a noisy Molineux has on the team.”