Hazard has informed Chelsea of what he plans to do at the end of the season and, with no agreement yet reached to extend his Blues contract beyond 2020, he is widely expected to complete a switch to the Santiago Bernabeu.
The 28-year-old has spent seven seasons as a Chelsea player, winning two Premier League titles, the FA Cup, the Carabao Cup and the Europa League, but he said victory in this season's final and the promise of Champions League football next term would not be enough to keep him in west London.
Loftus-Cheek has joined a number of Chelsea stars in expressing his appreciation for Hazard and admitted he has adopted the song that has been ringing around the club's stands in recent weeks.
"I've been singing that to his face, in the dressing room!" Loftus-Cheek told Sky Sports .
"I'm sure everyone at the club wants him to stay – players, fans, staff, management included.
"He's such a talent and a player who has contributed to the club massively over the last seven years, the titles he has helped the club win. Everyone has enjoyed watching him play over the past seven years.
"I'm sure the club thanked him for what he's done and if he does decide to move on then I wish him all the best."
Chelsea defender David Luiz echoed Loftus-Cheek's call for Hazard to stay, while comparing the forward's predicament to his own when he left Stamford Bridge five years ago.
"I want him to stay also, of course," said Luiz. "He's a great player, I want him to play with the best. I think he has to decide.
"I decided for myself when I left Chelsea for PSG. It was not easy for me, but it was a decision I took in the moment because my contract was finished.
"I was trying to feel a different challenge, and everyone here was respecting that, so I just respect Eden also.
"He has to decide for himself. He's a great player, a great friend of mine. I just wish him all the best, but I hope he can stay with us."