The Belgium international has long been linked with a move to the Liga giants, with his profile and ability considered to fit the ‘Galactico’ mould.
He further underlined his value to the cause with a match-winning performance in an FA Cup final victory over Manchester United, and Hoddle believes it is imperative he stays put.
The former Blues player and manager wrote in a column for the Daily Mail: “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.
“Hazard was excellent, even though I've seen him play better, he was able to get away from Ander Herrera and we saw the consequences when Phil Jones brought him down for the vital penalty.
“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.
“The problem for Chelsea is that their current squad is not good enough to compete in the Champions League and Premier League. Manchester City can do it, Chelsea can't, and that's why you've had these seasons where the Premier League form is poor if they are in Europe.”
Hoddle added, with Conte’s future continuing to be called into question despite countering a frustrating fifth place finish in the Premier League with more major silverware: “As a former Chelsea manager, I am very interested to see what Roman Abramovich and the club do next. It's OK to let managers leave if they have been unsuccessful, but you can't call Conte that.
“Maybe Chelsea think the pattern of changing managers without impacting on trophies will carry on. It's a big call.
“Whoever the next manager is, there has to be a reshuffle in the squad. First of all, Hazard can't be expected to provide the 'Wow' moments all on his own. And secondly, if recruitment is poor, he is going to wonder why he wants to stay at a club without Champions League football again.
“And on Saturday's form, there will be no shortage of takers for the Belgian star.
“Ideally, Conte and Hazard might be at The Bridge next season. But Hazard has to be.”