Hernandez joined Los Blancos on a season long loan from Manchester United in September but has been frustrated with the lack of playing time in such a competitive squad.
He has made just 13 appearances for Madrid this season, 12 of which have come from the bench and the Mexican has scored three times.
The Daily Mirror are reporting that Southampton are interested in bringing Hernandez in to bolster their current frontline, which boasts the likes of Saido Mane, Shane Long, and Graziano Pelle.
The Saints are said to be in tough competition to sign the 26-year-old forward from Premier League rivals Manchester United though, with the likes of Stoke, Wolfsburg and both Inter and AC Milan reported to be interested.
Hernandez has the potential to score bags of goals given the chance of a lengthy run in the side. His Premier League experience makes him ideal for any top flight club chasing him.
He has scored 37 goals in 102 Premier League games, and more than half of those games have seen him start on the bench.
It doesn’t look likely that Hernandez will return to the Manchester United setup on a permanent basis and many clubs would relish the chance to sign him.
Southampton have enjoyed a fine season under Ronald Koeman and are just six points off fourth spot with eight games to play.
Would Javier Hernandez be a good signing for Southampton?