The 25-year-old returned to Merseyside after spending most of the last four months in the United States, where he underwent an operation in April.
It is understood Sturridge began training again at the club’s Melwood base on Monday but he is currently working to an individual plan.
While that does involve some ball work, Sturridge has yet to rejoin the main squad.
When Sturridge underwent surgery his return to competitive action was predicted to be around October but earlier this month manager Brendan Rodgers said he hoped the striker would be back by early September.
Sturridge made only 18 appearances last season after being plagued by thigh, calf and hip problems and while he has been away rehabilitating, Rodgers has spent #32million on Aston Villa’s Christian Benteke, who has played every minute of the Premier League campaign so far and opened his account with a controversial winner against Bournemouth last week.
Two other new summer recruits – full-backs Nathaniel Clyne and Joe Gomez – have also settled in well and impressed first-team coach Gary McAllister.
“For two guys that have just arrived at the club, where the expectation level will be way above what they’ve experienced before, they already look as though they’ve been here a long, long time,” he told liverpoolfc.com.
“The fortunate thing is Liverpool have got them right at the start of hopefully what can be long, long careers here.
“You don’t want to put pressure on players. Nathaniel obviously has already made it through to the international set-up and Joe Gomez has in the younger age groups, but they both look as though they will go on to play (regularly) at that level comfortably.
“They’re keen to learn and very young – age is on their side, definitely.”