The Belgium international was linked with a move to the Champions League holders in the summer transfer window.
However, Hazard remained at Stamford Bridge following Zinedine Zidane’s departure at Real Madrid.
The 27-year-old has scored five times in five games in the Premier League this season to hit the ground running.
Hazard netted his second-ever Chelsea FC hat-trick in a 4-1 win over Cardiff City in the Premier League last weekend.
The Chelsea FC number 10 will have 12 months left to run on his Blues deal next summer unless he agrees a new deal during the current season.
The Blues forward came off the bench to score a brilliant winner in a 2-1 win over Liverpool FC in the Carabao Cup third round on Wednesday night.
Former Liverpool FC defender Carragher believes Chelsea FC will be worried about Hazard’s contract situation.
“There’s definitely going to be a question asked in January or at the end of the season when he will only have 12 months left. Then you are into that Thibaut Courtois territory and he ended up going to Madrid,” Carragher told Sky Sports.
“I’m not trying to get Hazard out of Chelsea, but when Madrid or Barcelona come for one of your players it’s so difficult to keep hold of them because it’s every player’s dream, certainly foreign players. Liverpool have had that with Xabi Alonso and Luis Suarez and even Cristiano Ronaldo left Man United. I think Chelsea will have a problem in the summer.”
Chelsea FC will host Liverpool FC in their next Premier League fixture at Stamford Bridge on Saturday evening in the top of the table clash.
The Blues haven’t won the Premier League title since 2016-17 under Antonio Conte but Chelsea FC did win the FA Cup last term.
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