Across his six-year spell with Chelsea, the Belgian has been linked with a move away from Stamford Bridge on numerous occasions but another year without Champions League football could be the final straw.
The Blues finished in fifth place in the Premier League table to miss out on a spot in the Champions League for the second time in three seasons.
A major sticking point for the potential transfer could be Atletico Madrid's unwillingness to sell, and a release clause of £87m would make this an extremely expensive option for Chelsea should they look to make a move this summer.
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"I think he's our best player", Fabregas said of his teammate after reaching Perth ahead of Monday's friendly against Perth Glory.
A number of new players could wear the kit this season, with Jorginho having already been secured from Napoli, their first signing under new manager Maurizio Sarri, and the club keen to acquire Daniele Rugani from Juventus. "He is the best player at the club and we need at Chelsea to keep the best players".
"It's for the club and Eden to decide but for us he is the most important player and we want him to stay".
"Everyone loves him - the fans, the club, the players, and we need him".
Chelsea are in Australia on tour, while Hazard rests after his exploits in Russian Federation, and Fabregas says his team-mate is integral to the club.