According to Tomas Andreu of Sport, Hazard is 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.
The Blaugrana have the money to pay Hazard's transfer fee and his wages, with Paulinho's recent return Guangzhou Evergrande expected to boost the club's coffers significantly if the transfer is made permanent.
Genuine progress on a deal to sign Hazard, 27, is unlikely to occur until Belgium finish their 2018 FIFA World Cup campaign—they still have a third-place play-off against England on Saturday.
Chelsea's managerial situation also likely needs to be resolved before his sale could be sanctioned.
Antonio Conte is still in charge of the west London club but looks set to be imminently replaced by Maurizio Sarri, per Sky Italy (via Sky Sports' Kaveh Solhekol):
The Blues would be loath to let Hazard go, as he has arguably been their most vital player over the past few seasons.
However, given his calibre, Hazard may well be eager to make a move to a UEFA Champions League club that is likely to win major silverware.
La Liga champions Barcelona fit that bill perfectly. Chelsea do not.
They finished fifth in the Premier League last term, 30 points behind champions Manchester City, meaning they will play in the UEFA Europa League next season.
Per Andreu, one of the main obstacles to signing Hazard this summer could be competition from elsewhere, specifically Real Madrid, who need to make a marquee signing after selling Cristiano Ronaldo to Juventus.