Speculation around the Belgian forward has been building for some time.
He has regularly been linked with a switch to Spain, and the expectation is that a deal will finally be pushed through this summer.
Hazard is approaching the final year of his contract at Stamford Bridge and Chelsea know they must sell now if they are to generate a fee close to what the 28-year-old is worth.
Mourinho, who has previously managed the Blues and Blancos, believes an agreement will be reached and a talismanic presence will depart west London.
He hopes that move will be made with Chelsea having secured more major silverware, with domestic rivals Arsenal set to provide their opposition in a continental showpiece on May 29.
Mourinho told Sky Sports: “It looks like it is the last match in blue for Eden Hazard.
“He is a player that was crucial for Chelsea's success in this last generation and Eden also will try to be what he is the majority of the time - a fantastic player on the pitch.
“He will want to win and possibly go to Real Madrid with a last trophy for Chelsea.”
Mourinho believes Maurizio Sarri’s side are well placed to get their hands on the Europa League crown.
Chelsea have already secured Champions League qualification for 2019-20 through a third-place finish in the Premier League, meaning that there is more pressure on Arsenal to deliver.
The Gunners could only end their domestic campaign in fifth spot and are aware that they need to emerge victorious in Baku in order to rejoin the European elite for next season.
“More pressure on Arsenal because they want the Champions League spot for next season,” added Mourinho.
“They play for many millions so more pressure on the Arsenal side.”
Mourinho will be an interested spectator of events in Azerbaijan as he continues to ponder his next move.
The Portuguese has been out of work since leaving Manchester United in December 2018 but has expressed a desire to return to coaching this summer.