Ghoddos is on an expiring contract with Brentford and the club has previously confirmed that there will be no continuation for the player after the summer.
Ghoddos, 30, has also been linked with a move to Malmö FF and in an interview with Fotbollskanalen, sporting director Daniel Andersson has confirmed that there is contact between the parties.
Now, Ghoddos is instead considering a move within England – and to remain in the Premier League.
Media reports suggest that Ghoddos is about to sign a contract with Southampton, who gained promotion to the Premier League after defeating Leeds United in the playoff final at Wembley.