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.
Liverpool 
Tottenham 
Eintracht Frankfurt 
Bayer Leverkusen 
AC Milan 
Genoa 
Nizhny Novgorod 
Spartak Moscow 
Valencia 
Alaves 
Feyenoord 
Pec Zwolle 
Roma 
Juventus 
Sevilla 
Granada CF 
Famalicao 
Benfica 
CSKA Moscow 
Rubin 
Lokomotiv Moscow 
FC Rostov 
Udinese 
Napoli 
Crystal Palace 
Manchester Utd 
Lille 
Lyon 
Paris Saint Germain 
Borussia Dortmund 
Real Madrid 
Bayern Munich 
Club Brugge 
Fiorentina 
Atalanta 
Marseille 
Catanzaro 
Sampdoria 
Concarneau 
Bordeaux 
Frosinone 
Inter 
Fulham 
Manchester City 
Celtic 
Rangers 
Borussia Monchengladbach 
RB Leipzig 
Werder Bremen 
Krasnodar 
Everton 
Sheffield Utd 
Burnley 
Villarreal