The Belgium international has little over 18 months left to run on his current deal to raise questions about his long-term future at the west London side.
Hazard has been linked with a move to Real Madrid over the past 12 months or so, while los Blancos have been touted as an interested party over the past four or five seasons.
The 27-year-old made a brilliant start to the Premier League season following a return of seven goals in eight games in the top flight to hit the ground running under Maurizio Sarri.
However, Hazard suffered an injury setback in a 2-2 draw with Manchester United to curtail his momentum and prompt a run of eight league games without a goal.
But the Chelsea FC number 10 scored one goal and made an assist in their 2-1 win at Brighton and Hove Albion last weekend before a 1-0 home loss to Leicester on Saturday.
Sky Sports reporter Sheth believes Chelsea FC will remain firm and refuse to consider selling Hazard in the January transfer window.
“Conclusion to a saga involving Eden Hazard? I don’t think so,” Sheth told Sky Sports’ Transfer Talk podcast.
“I can’t see Chelsea selling Hazard in January with them fighting for a top-four place. He could be the difference between them getting top four and not.”
Hazard moved to Chelsea FC in a big money deal from Lille in the 2012 summer transfer window.
The Blues forward has won two Premier League titles, the FA Cup, the League Cup and the Europa League at Stamford Bridge.