During the World Cup in Russia, Hazard revealed he was considering leaving the club he had joined from Lille in 2012 but Fabregas has begged him not to go.
"I think he's our best player," Fabregas said of his team mate after reaching Perth ahead of Monday's friendly against Perth Glory.
"We are a top club, we want to be a top team, we want to win things, and for that you need your best players. Eden is one of them.
"He's a player that we all love to play with, especially me. For us, he's our most important player.
"Everyone loves him -- the fans, the club, the players, and we need him. He knows that," the Spaniard added.
Monday's match is Chelsea's first under new coach Maurizio Sarri, who has promised an attacking brand of football and Fabregas cannot wait to see how it unfolds.
"It's a way of football that I believe in, that I really like, that I grew up in this system," the 31-year-old said.
"For the type of player like myself, we can take a lot of advantage."
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
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