Hazard is currently locked in talks over a new contract at Stamford Bridge after a stunning start to the season.
But he has also been linked with a move to Real Madrid after his comments in the summer suggested it was time to move.
Chelsea are looking at ways to lock him down into a new deal and will offer him £300,000 a week wages and could also make him club captain.
Gary Cahill is currently out of the side with Cesar Azpilicueta taking the armband for most of the season.
But Hazard, who captains Belgium, is a long-term candidate if he signs a new deal to signal his intent to stay.
And when asked about the captaincy, Hazard said he would find it difficult to say no but that he thinks others are more deserving of the honour.
“Yes, I don’t want to say no of course,” he told Sky Sports when asked if he would like to be captain.
“But I think some of the players deserve more to be captain than me.
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“I mean outside football I always try to give everything for the fans, like in interviews I try to be an example, so if I’m the captain I would be happy.”
Hazard was also quizzed on his leadership skills and insists despite his quiet nature he tried to lead by example.
“On the pitch since five years or six years I feel like I’m the leader on the pitch,” he added. “I’m the captain of Belgium but I don’t like to talk a lot.
“On the pitch I hope I show the right way to win.”
And Chelsea boss Maurizio Sarri hopes he will sign him new deal ‘immediately’.
The Blues are ready to make Hazard one of the top earners in England and know much of their future aspirations rest on his shoulders.
“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.”
Hazard appears caught between wanting to stay and go.
In the summer he revealed he thought it was time for a new challenge before ultimately staying.
This season he has said he could stay at Chelsea for the rest of his career, but has appeared hesitant to sign a new deal.
Former Chelsea midfielder Jason Cundy urged the club to offer him even more money.
Speaking in October he said: “I would make him the highest paid player in the world.
“I would give him £650k, £700k, £750k-a-week. Why not? Tell me why not?
“To replace him… you can’t replace him!
“What’s he worth on the open market, say £150million? You’re not going to be able to replace him!”
Published at Wed, 05 Dec 2018 08:12:00 +0000