Hazard is expected to join the Spanish giants this summer in a big-money move after the player confirmed he was leaving at the end of the Europa League final.
Ramos was himself linked with a move away from the Bernabeu after a reported breakdown in his relationship with president Florentino Perez.
But he has since reassured fans he will be staying, before calling on the club to sign Hazard.
“Eden Hazard is a top player who would give us a lot.
“I hope he comes, he could give us a lot.
“I am staying at Real Madrid. I’m going on holiday now and will see who we have signed and who we have not.
“I’m not looking to renew (my contract), I am happy with what I have and I hope these comments mean the “Ramos stuff” is now finished,” Ramos told a press conference on Friday.