The Saints, however, face strong competition from Stoke City whose misfiring forward line has seen them slip towards the relegation zone.
Sturridge is 4/1 to join Southampton in the transfer window with Liverpool refusing to consider a loan move unless there is a permanent deal at the end of it.
The England striker is concerned that the fee set by Liverpool will be unrealistically high with the Reds spending £75m on Virgil van Dijk, 26. Having been forced to pay a world record fee for the defender, the Reds may be tempted to recoup some of that money in Sturridge’s sale.
Stoke are desperate to add to their squad with Saido Berahino currently in a miserable 36-game scoreless run.
Sturridge has scored just twice in his nine appearances this season although he has been predominantly used as a substitute with Liverpool’s triumvirate of Mane, Firmino and Salah in spectacular goalscoring form.
With Harry Kane in scintillating form for his club, Sturridge knows his current situation isn’t doing his England aspirations any favours. Gareth Southgate has made it clear to other players that they won’t be selected if they aren’t in their club sides.
With a World Cup finals next summer, it’s little surprise that the former Manchester City and Chelsea striker is looking for a new club.