The Blues could definitely do with a quality attacking player like Bale in their ranks if they are to lose Hazard anyway, which will look increasingly likely the longer he goes without signing a new contract.
Hazard’s current deal is due to expire at the end of next season, and Marca report he’s turned down various offers of renewing and is confident of getting his dream move to the Bernabeu.
Meanwhile, Chelsea are among the clubs being linked with Bale, along with top four rivals Manchester United, even though the Express recently claimed the player himself was not so keen on leaving Spain.
The Wales international has shone in the Premier League in the past, though he’s also won a huge number of big trophies with Real, even if he’s never been quite as important a player for them.
Bale did manage to score twice in last season’s Champions League final win – enabling him to pick up the famous trophy for the fourth time since he joined the club in 2013.
Overall he’s also scored 92 goals for Los Blancos – a decent record for a player who doesn’t play as an out-and-out striker.
It’s unlikely the 29-year-old would come close to replicating that at either Stamford Bridge or Old Trafford, but Don Balon claim Madrid want to offer him plus £44million to Chelsea for the Hazard transfer.
While Chelsea and Hazard might go for that, it remains to be seen if Bale himself can be persuaded.
If CFC can snap him up it would be a big blow for rivals United, who remain linked with the player by the Express and who could urgently do with an upgrade on out-of-form attackers like Alexis Sanchez and Marcus Rashford.