A move to Spain has not worked out as planned for a man who illuminated the Premier League across seven years at Stamford Bridge.
Real invested €100 million (£89m/$119m) worth of faith in Hazard when prising him from Chelsea’s clutches.
The plan was that the 29-year-old would fill the role of Blancos talisman that had been vacant since Cristiano Ronaldo departed in the summer of 2018.
The 2019-20 campaign was, however, to be a testing one for Hazard as he struggled to find a spark.
Injury struggles did his cause few favours, but he managed just one goal through 22 appearances.
Azpilicueta, who spent many successful years alongside Hazard in west London, believes a proven performer will deliver for Real in 2020-21 if he remains fit and rebuilds lost confidence.
The Chelsea defender told Radio Marca: “This season has been hampered by injuries and he hasn't been at 100 per cent.
“I hope he can pick up some rhythm in order to help his team.
“I have no doubt that Real Madrid have lots of quality players and that Eden can show his worth in that team.
“Let's hope we can see the Eden we saw at Chelsea.”
While Hazard is looking to become a star turn in La Liga, it could be that the Spanish top flight soon bids farewell to its biggest attraction.
Lionel Messi continues to spark exit talk at Barcelona, with the Argentine having informed those at Camp Nou that he wishes to move on.
The Premier League has been mooted as a potential destination for the six-time Ballon d’Or winner, with Manchester rivals City and United apparently in the mix.
Azpilicueta would like to see the mercurial Argentine in England, even if he represents a rival outfit, with excitement building regarding a stunning switch.
“For us, it would mean much more competitiveness, but it would be strange not to see him at Barcelona next season,” added the Spaniard.
“In England, there is a lot of expectation about this topic. We will see what happens.”