Hazard has been one of the players of the tournament as Belgium reached the semi-finals for the first time since 1986, before losing 1-0 to France.
The 27-year-old’s future is uncertain at Stamford Bridge, where manager Antonio Conte was finally sacked on Friday after falling out with the board and senior players last season.
Real are said to be considering Hazard as a replacement for Cristiano Ronaldo after the five-time Ballon d’Or winner joined Juventus this week.
“He’s one of the most complete footballers in the modern game,” Martinez said on the eve of Belgium’s third place play-off against England in Saint Petersburg.
“He’s probably one of the best footballers in one-v-one situations. He brings that understanding of how to break defensive systems down.
“I think the biggest aspect I can tell you that not many people can know is his incredible personality and his leadership.
“For a footballer who lives in the box and to score goals, he’s someone who never drops his standards.”
Hazard has won the Premier League title twice with Chelsea, in 2014-15 and 2016-17, since joining from Lille six years ago.
“He’s someone who’s got a winning mentality and he can play in any demanding team or club around the world,” added Martinez.
“As a footballer now with the maturity he has, you can build a winning project around him.”
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