The former Chelsea goalkeeper believes the Belgian will be as good as the Barcelona and Real Madrid stars in the years to come.
The Belgian star has had an impressive season with the Blues, with his latest vital contribution seeing him score the winning goal in a crucial victory over Manchester United last time out.
Such has been the level of his performances, he is widely expected to be named PFA Player of the Year come the end of the season, while Brazilian legend Pele recently claimed the player would break into Ronaldo and Messi territory once he had performed consistently at the highest level.
Schwarzer, who was a teammate of the forward at Stamford Bridge prior to agreeing a move to Leicester City, agrees with the legend’s statement.
“Who are we to argue with Pele? I have to agree with him,” he said.
“If he keeps doing what he’s doing then there’s no doubt in my mind that he’ll be able to be compared with Messi and Ronaldo.”
The Australian keeper does, however, admit that Hazard still has some way to go until he reaches the level of the La Liga duo.
Both Messi and Ronaldo have arguably been the best two players on the planet for the last few years, often going head to head for the Ballon D’Or and breaking league and European records on a consistent basis.
Hazard isn’t quite at that level yet, but his improvements on last year have impressed Schwarzer nonetheless.
“He’s still got some way to go but he’s a phenomenal player. This season alone the step up from last season, in term of his consistency and level of play, has been extraordinary,” he added.