The 36-year-old still has one year remaining on his contract at Elland Road, but he is set to be released by Leeds after an injury-hit season meant that he only made 16 Premier League appearances for Marcelo Bielsa's side during the 2020-21 campaign.
It is believed that Hernandez wishes to return to Spain, where he last played in 2016 while on loan at Rayo Vallecano, after also playing for Valencia and Getafe in La Liga earlier in his career.
Spanish outlet Marca report that Cartagena are the favourites to land Hernandez's signature, with the Spanish side's fans hoping the Castellon-born playmaker can link up with Pablo de Blasis in attack.
Cartagena are in need of some attacking inspiration for next season to improve on their 16th-placed finish in the Spanish second tier last season.
Hernandez became a fan-favourite during his five-year spell with Leeds, scoring 36 goals and providing 42 assists in 175 appearances for the club, and achieving promotion to the Premier League last year.
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