The skillful forward has just two years left on his current deal with Chelsea and is stalling over signing an extension.
While the Blues are not keen to sell him, there are suggestions Hazard is considering his future and will take a decision based on the kind of players Chelsea sign this summer.
But according to Sport, the Belgium global is one of Barcelona's priority targets and the club made their first approach to Hazard's representatives last week.
Mbappe has arguably been the stand out attacking player at the World Cup in Russian Federation, despite only being 19-years-old and rumours have been circulating for some months now that PSG may be forced to pull out of the deal they agreed with Monaco at the end of last season.
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It's also claimed that Hazard believes now is the right time to leave Chelsea in order to further his career and win more titles.
According to Tomas Andreu of Sport, Hazard is now Barca's main attacking target after they missed out on Antoine Griezmann, and he is interested in the prospect of making the switch to the Camp Nou.
Speaking on Monday, Hazard suggested once again that he would be open to joining Real Madrid this summer.
"Zidane is someone special, it's true, but I think Real is everyone's dream".
According to the same story, the Blues won't resume negotiations with the Belgium worldwide over a new deal for at least another week following his participation in the World Cup. "But the blue shirt suits me well, so everything's fine, and staying doesn't bother me".