The 32-year-old's last switch was from Chelsea to Real Madrid in the summer of 2019, and the Belgian since made 76 appearances for Los Blancos, scoring only seven times.
With his contract at the Bernabeu set to run until the June 2024, it was announced that both the player and Real had agreed to a mutual termination of the terms, meaning Hazard is now a free agent.
A mixture of poor form and injuries meant the former Lille man played just six La Liga matches for Carlo Ancelotti's men last term, starting just two and only getting a single goal contribution.
According to Football Espana, Inter Miami are interested in securing the services of Hazard this summer in order to make him another marquee capture for the club.
It is understood that the Herons are in the process of convincing the attacker to leave European football for the first time in his 17-year professional career and move to MLS.
The report claims that Inter Miami are not the only side keen on bringing Hazard into their ranks, meaning Javier Morales's men could face some fierce competition in the race for the Belgian.
Inter Miami are currently rooted to the bottom of the Western Conference in MLS, with a poor start to the campaign leading to the end of Phil Neville's time as manager.
Currently nine points behind ninth-placed CF Montreal, Morales's charges have significant work to do in order to reach the playoffs later this year, although they are set to have some major enforcements.
The club - founded only in 2018 - recently announced the signings of former Barcelona duo Lionel Messi and Sergio Busquets as they attempt to become a top side in MLS.
The Argentinian World Cup winner is yet to make his debut for Inter Miami but is scheduled to do just that when the Herons travel to Mexican outfit Cruz Azul in the Leagues Cup on July 22.
Hazard may not be the only ex-La Liga star to turn out at DRV PNK Stadium in the coming weeks, as the report adds that Miami are also interested in Jordi Alba, Sergio Ramos and Andres Iniesta.
Ramos is a free agent after his two-year contract with Paris Saint-Germain expired this summer, and the centre-back is reportedly in advanced talks with Inter Miami over a move to MLS.
Morales will take his side to DC United on the weekend looking to end a run of nine matches without a maximum in MLS - the current group of players cannot afford to wait for Messi before picking up points.