The 23-year-old was stretchered off with an ankle injury during England's 1-1 friendly draw with Republic of Ireland at Wembley in May.
The Reds are now back in pre-season training and, while Sturridge is still sidelined, the club's head of performance, Glen Driscoll, is happy with his progress.
|5/1||Liverpool are 5/1 with BetVictor to sign Alex McCarthy from Reading
"Steven Gerrard is still being modified but he's about to enter all out training."
Driscoll was also upbeat on the health of the other members of the squad who are returning to training after injury.
"Martin Kelly is back in full training and doing really well," he added. "He has absolutely no problems.
"Raheem Sterling has actually come back a little bit earlier, like Martin, to do some extra conditioning so they hit the ground running. He looks extremely sharp.
"Joe Allen also did some extra work and is raring to go now."
Liverpool kick off their 2013-14 campaign at Anfield against Stoke City on August 17.