The 28-year-old said earlier this year that he has “made a decision” over his future, fuelling speculation that he will be heading to the Bernabeu at the end of the season.
However, Drogba – who won four Premier League titles, four FA Cups, three League Cups and the Champions League over two spells at Stamford Bridge – thinks Hazard can realise his dreams by staying put.
"Why [should he leave]?" the Ivorian told Omnisport.
“I think he can have this here in Chelsea.
"You know, I had many opportunities to leave and I decided to stay to make my own story and win the Champions League here. I think he's got a chance to make his own story.
"This club is still young and we need people like him to improve the quality in terms of Champions League trophies in the room, he can help us.
"I will be very happy if he stays here, but if he goes to Madrid, good luck to him."
Drogba also backed his former manager Jose Mourinho to return to the top after he was sacked by Manchester United in December.
"I think Jose is a great manager," Drogba said.
"I think he deserves the chance to manage again and I think he will. He is passionate about his job.
"You know, it's unfortunate what happened with Man United, but he still has the quality to manage a team.
"We know he did it many times and people forget that the year before he won the Europa League with this team and suddenly everyone says he is done."
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