Hazard has long been linked with the Champions League holders and his performance to win Chelsea the FA Cup on Saturday will do little to dispel those rumours.
However, for Hoodle, the key aspect of a potential deal could be Gareth Bale. It's been suggested that the Welsh forward was heading for Real's exit door but a recent resurgence of form could see that thrawted.
Florentino Perez could still make a move for the 'Blues' midfielder, aided by his opposition's failure to qualify for the Champions League, but Hoodle insists Chelsea must try and keep Hazard at Stamford Bridge.
In his column for the 'Daily Mail', he wrote: "If keeping [Antonio] Conte may be beneficial to Chelsea, keeping Eden Hazard is absolutely crucial. He's the most important person in the Chelsea dressing room going forward and the Cup final proved that.
“The biggest European clubs would have been watching. I know Barcelona look likely to sign Antoine Griezmann but you could see Hazard fitting in at Real Madrid. He isn't Lionel Messi or Cristiano Ronaldo but for me he's among the top five players in the world, he has that X-factor that causes danger every time he's on the ball.
“If Gareth Bale leaves Madrid, you could see them wanting Hazard, and it's vitally important Chelsea don't allow that to happen and make the kind of signings that will want him to say. It's even bigger than keeping Conte.