Hazard signed a five-year contract with Madrid in 2019, joining for a reported initial fee of just over €100million after seven successful years at Stamford Bridge.
However, injuries have blighted the Belgium star's time in Spain, and he has only started 21 LaLiga matches over the past two seasons.
Hazard made the first XI only 11 times in 2020-21 in all competitions, scoring four times and providing two assists, while footage of him sharing a joke with former Chelsea team-mates after Madrid's Champions League semi-final defeat infuriated fans and media in the Spanish capital.
It has been reported Madrid are prepared to cut their losses on Hazard and listen to offers in the region of €50m in the next transfer window, but the 30-year-old is not prepared to give up on his Santiago Bernabeu career.
"I still have three years of contract at Real Madrid. I like the club. I like the players. I will give everything next season for this club. I don't see myself leaving Real Madrid now," he said on Monday.
"We all know the first two years has been bad because of the injuries. I know myself and I know if I'm fully fit, I can do great things for this club.
"First of all I want to think about the Euros, then I'll give everything for this club next season. That's my club.
"I still have good years ahead of me. I was injured at Chelsea and came back to a good level. I just need match rhythm. I don't have many minutes in my legs."
Asked to sum up his season, Hazard replied: "Unlucky.
"Everything has gone well since the start of my career. I've never had many injuries. It's been different for a year and a half.
"I know I can't put everything down to bad luck, but there's been a lot. The coronavirus crisis, the injuries. I was always strong when I could play lots of matches in a row; now, that wasn't possible.
"I'm close to my good level. I just have to get match rhythm now. I'll do everything I can not to get injured."
Hazard is with the Belgium squad preparing for friendly matches against Greece and Croatia this week.
Roberto Martinez's side begin their Euro 2020 campaign against Russia in St Petersburg on June 12.