The 23-year-old was substituted while playing for England in last week's 1-1 draw against the Republic of Ireland at Wembley after apparently sustaining ankle ligament damage.
Reports have suggested Sturridge could be out for three to four months, which would mean he would miss the start of next season, but Press Association Sport understands it could be at least another 48 hours before Liverpool's medical staff will have a full picture of the extent of the injury.
Sturridge scored 11 goals in 16 appearances after joining from Chelsea in a £12million January transfer, becoming the club's fastest player to 10 Premier League goals - taking just 13 matches to beat previous holders Robbie Fowler and Fernando Torres by five games.
With fellow striker Luis Suarez banned for the first six matches of next season - even if he is still at the club - having Sturridge unavailable as well would be a significant blow.
There could be a number of developments this week as the club are still awaiting a decision from striker Andy Carroll on whether he wants to move to West Ham, while Celta Vigo forward Iago Aspas is set to have a medical later this week ahead of an £8million move.
While Sturridge's participation in the early part of next season remains in doubt, manager Brendan Rodgers will at least be back up to full strength in central midfield. He lost Joe Allen and Steven Gerrard to shoulder problems in the last three months of the campaign but, after both had surgery, the pair will be ready for the start of pre-season.
Allen, who started brightly but faded in his first season after a £15million move from Swansea is hoping to take further inspiration from Gerrard. The Camarthen-born midfielder suffered after being given the unwanted tag of the 'Welsh Xavi' for his ball-retention qualities playing for Swansea.
Wales international Allen was answering questions on the club's Indonesian Facebook page, and said: "Xavi is a player I admire so it was very flattering, but I've got a bit of work to do to get up to his standards.
"But having the chance to play alongside someone like Steven Gerrard is inspiring: (not only) the level of talent and ability but also professionalism he brings is first-class and that's why he's one of the best players in the world."