Ronald Koeman's men are considering a move for the Manchester United striker, who would cost around 15 million pounds, but may face competition from Atletico Madrid.
The club has renewed its interest in the Mexico international after attempting to sign the 26-year-old in January, when the Red Devils informed Hernandez he could go out on loan.
Then-manager David Moyes subsequently pulled the plug on a potential move away, but new boss Louis van Gaal has refused to rule out an Old Trafford exit for the striker.
When asked after the friendly win in Washington whether he would consider selling Hernendez, Van Gaal told reporters: “That I cannot answer because he is a player of Manchester United at this moment.”
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Southampton, meanwhile, has cash to spare after selling Luke Shaw, Adam Lallana, Dejan Lovren, Rickie Lambert and Calum Chambers, and with Tottenham reportedly keen on Jay Rodriguez and Morgan Schneiderlin.
Manchester United is believed to want around 15 million pounds for Hernandez, who joined Manchester United from Guadalajara in 2010 and has become a fan favorite at Old Trafford.
Southampton may face competition from abroad, however, with Spanish champion Atletico Madrid interested in the Mexico international and manager Diego Simeone acknowledging a move could happen.
"With Javier Hernandez and plenty of other great players, anything is possible. We can't close the door to anyone until the transfer window closes,” he said.
Hernandez has also been linked with a move to Inter, where he would link up with former captain Nemanja Vidic, and said he was happy to hear of the Serie A side’s interest.