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 six 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.
Daily Record journalist McGarry confirmed that FC Barcelona, Bayern Munich and Real Madrid are keeping tabs on Hazard.
“My information is one of the reasons why he is so calm is because he has concrete interest, if not offers, from three of Europe’s biggest clubs – Barcelona, Bayern Munich and Real Madrid – for the season after this,” McGarry told the Transfer Window podcast.
“He may well choose one of those elite clubs to transfer to. The contract situation being what it is, Chelsea will be forced into the same situation as Courtois.”
Hazard has won two Premier League titles during his six season stay at the west London side.
The Belgian captain fired Roberto Martinez’s Red Devils side to a third place finish in the World Cup during the summer.
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