The player's representative, Marc Formeaux, has revealed the free-spending English outfit are keen on the Belgian international and may look to win his signature with an offer in January.
City could have the money to tempt Hazard, but the midfielder has already set his sights on moving to one of the continent's traditional giants in Real.
"In France, people are talking about an offer of €30m from City and that he would then be loaned back to Lille for free until June," AS quote Formeaux as saying.
He added: "His future is with one of European football's prestigious clubs like Real Madrid, Barcelona, Chelsea, Manchester City, AC Milan, Inter or Juventus.
"For Hazard, the president of Lille wants to receive €40m (£33.3m) while the player himself has declared that he wants to play for Madrid."
Formeaux also represents Rennes midfielder Yann M'Vila, who has been strongly linked with Arsenal, and he now has a value, according to the agent.
"Regarding M'Vila, he is valued at €20m (£16.6m) and he does not know where he wants to go," Formeaux said.
"In Italy, they have linked him to Inter and AC Milan, but we will have to see who can pay his price and then convince him to join them."
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