The Belgian scored twice in a 4-1 win over Arsenal in Baku on Wednesday to clinch the European title, before dropping a post-match hint that it was his final appearance for the Premier League club.
"I think it's goodbye but in football you never know,” he told BT Sport.
“My dream was to play in the Premier League and I did this for seven years in one of the biggest clubs in the world, and maybe it's time for a new challenge."
Spanish outlet AS believes that today, Thursday, will be decisive for the 28-year-old’s move to the Bernabeu.
Sources at the La Liga club have said that Real will make a definitive move to convince the Blues to sell their star asset, who is entering the final year of his Stamford Bridge contract.
Hazard himself wants to travel to the Spanish capital on Saturday, with plans in place for the winger to be presented as a Merengues player on Monday 3 June at the Bernabeu.
While Real chiefs have tried to put the Belgium international at ease over the situation, his representatives yesterday had some doubts.
Chelsea director Marina Granovskaia has a reputation as a tough negotiator, and the Blues’ impending transfer ban gives them a good reason to try to hold onto the player.
However, Real are convinced that their offer will be accepted, and the fact that Chelsea will risk losing the former Lille winger for free next summer if they don’t sell now also works to their advantage.
Hazard ended the campaign with 21 goals and 17 assists in 52 appearances across all competitions, the most prolific season of his time at Chelsea.
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