The Saints are preparing a £25m bid for the England international which would see Sturridge join initially on loan in January, with a view to a permanent move in the summer.
Sturridge has found himself reduced to a place amongst the Liverpool substitutes with Jurgen Klopp willing to let the injury-prone striker leave the club to make room for new signings, according to the Express.
Klopp has preferred Roberto Firmino in attack with Sadio Mane, Philippe Coutinho and Adam Lallana acting as support for the Brazilian.
Southampton manager Claude Puel is keen to find a regular partner for central striker Charlie Austin having lost Graziano Pelle and Mane in the summer.
Should Sturridge join the Saints he will be treading the well-worn path between the south coast and Merseyside, with the Reds signing Dejan Lovren, Lallana, Mane and Nathaniel Clyne from Southampton in recent seasons.
West Ham are also thought to be interested in the 27-year-old, as are Stoke and AC Milan, but the Hammers would also want to negotiate a loan deal first to assess his fitness before committing to a long-term deal.Reuse content