The report claims that the Saints are preparing a £7 million bid for the explosive winger.
West Ham have been locked in talks with Besiktas over the transfer of Gokhan Tore since the start of the transfer window but have yet to agree a transfer fee.
The Hammers made a loan offer with a buyout clause option but Besiktas have made it clear that they want a transfer fee on a permanent deal if Tore is to leave the club.
Besiktas want at least £13 million for the explosive winger who still has another two-years remaining on his contract.
The Turkish international does have Premier League experience having risen through the Chelsea ranks before his move to HSV and then Rubin Kazan before joining Besiktas.
Tore established himself as one of the most highly sought after players in the league under the stewardship of Slaven Bilic who coached Besiktas for two seasons before taking over at West Ham.