The England worldwide had been linked with a move away from Anfield this summer, however Liverpool boss Jurgen Klopp has this week said that he believes Sturridge could still have a role to play for the club.
The 28-year-old was loaned out to West Bromwich Albion last January but failed to make an impact at the Hawthorns outfit, failing to score in six appearances for the relegated club.
Sturridge has so far featured in all three of Liverpool's pre-season friendlies to date.
'I always said there is a future, it's about what we do in the moment. "At the moment it's all good and we don't have to make decisions", he told reporters.
Liverpool striker Daniel Sturridge has admitted that he is eager to stay at the club next season and fight for his place in the club's first team.
Liverpool will travel to the US later this month for the International Champions Cup, where they will face Borussia Dortmund, City and Manchester United.
Southampton want to sign Danny Ings from Liverpool FC this summer, according to reports in the British media.
"I am feeling great and can't wait to get the season under way".
"Pre-season is going well, so for me it's keeping my head down and building on that. We have the tour to come where we face some great teams like Manchester United, Manchester City and [Borussia] Dortmund".
The Sun, as quoted by the Daily Mail, is reporting that the Saints are keen on a deal to bring the striker to St Mary's from Anfield as they look to bolster their attacking options ahead of next season.