While Origi made a surprise loan move to VfL Wolfsburg towards the end of the summer transfer window, Sturridge remained on Merseyside.
But after averaging just 36.7 minutes per game over 14 appearances so far this season, he could not be aggrieved for seeking the exit ahead of the World Cup in 2018.
The Telegraph claim that the Saints are interested in a loan move for the 28-year-old, with Mauricio Pellegrino looking to bolster his attacking options.
“Southampton believe that a loan deal may be most viable and could appeal to all parties,” Jeremy Wilson writes.
The south-coast club are also touted with an interest in signing Fulham left-back Ryan Sessegnon, who has been on the Reds’ radar in recent windows.
Meanwhile, Origi’s lack of goals while on loan with Wolfsburg—scoring just four in 18 appearances—has seemingly not deterred the Bundesliga club.
The young Belgian has been operating in a wide role of late, but could shift back into a centre-forward berth following Mario Gomez’s move to Stuttgart.
And according to ESPN, Wolfsburg are working towards a permanent deal for Origi, whose prospects with the Reds have seemingly passed despite showing positive form since joining from Lille in 2015.
Sporting director Olaf Rebbe is said to have told German publication kicker that the club would “exhaust their possibilities” despite struggling in early negotiations with Liverpool.
“The people at Liverpool are merchants, no Samaritans,” he lamented.
“We will still try to exhaust our possibilities, alongside the player who feels well here.”
Another striker who is likely to leave the club in the new year is Danny Ings, with the 25-year-old failing to gain a foothold on the first-team squad since returning from long-term injury.
Given Ings’ precarious fitness, having missed the majority of the past two seasons, it is unlikely that any side would be willing to negotiate a permanent move at this stage.