Madrid are said to be long-term admirers of Hazard, who has scored eight times and provided seven assists in 19 appearances for Chelsea during the 2017-18 campaign.
Essien has conceded that the Spanish giants will be a big draw for Hazard, but the 35-year-old is hopeful that the Premier League champions will be able to tie the Belgian international to a new long-term contract.
"He could go to Real Madrid to win the Ballon d'Or easier," Essien told Goal.com. "When we talk about Eden, he is such a good player. He's very quick, very good on the ball. He's very strong, he may be little but he is strong, trust me! It is hard to get the ball off him.
"He's such a good player and we're happy to have him at Chelsea but I'd understand why Madrid would be looking at him. He is proving it week-in, week-out. At the moment he is the most important player [at Chelsea]. When you have Hazard, he can always do something.
"He can always create something to do something with the ball. He makes goals for himself or others. He has that magic touch. I think that Chelsea need to renew his contract. You don't want your best players to leave and we need him at the club.
"I think he is only motivated about playing football, he just enjoys playing football. It would take a lot of money to replace him [at Chelsea] but I hope that they can tie him down for a long time."
Chelsea will look to continue their pursuit of Manchester City and Manchester United in the Premier League table when they travel to West Ham United on Saturday afternoon.