In outshining Brazil's Neymar in the last eight, Hazard may have put himself in the shop window.
According to Spanish outlet Sport, Barcelona have been exploring the possibility of getting Hazard on-board and also tempt him with the opportunity of him playing in the Champions League next term.
Hazard has been linked with a move to Real Madrid since the end of the season and he is expected to replace Cristiano Ronaldo who could leave to Juventus.
Speaking on the Transfer Window podcast last week, he said: "Chelsea have gone into this window preparing for the possibility they could lose Eden Hazard and Willian due to their contract situations - both in need of renewals - Willian has two years left". France vs Belgium will be interesting.
Although Hazard did remain tight-lipped when the subject of Real Madrid was mentioned insisting that he will have to see after the World Cup.
Hazard inspired Belgium to book a place in semi-final spot with France on Tuesday night.
"It is true that [Zidane] is special, but Madrid makes everyone dream".
Les Bleus have Mbappe in their ranks, meanwhile, with the Paris Saint-Germain striker becoming his country's youngest ever World Cup scorer earlier in the tournament.
"I'm fine at Chelsea and, for now, nobody has presented me with an offer, " he added.