The 29-year-old has been sidelined since sustaining the problem in a pre-season friendly against Atletico Madrid but is finally closing in on a return to action.
The England man spent a period of his rehab at the Aspire clinic in Qatar but has now returned to Melwood where he will continue his recovery with Liverpool's own medical staff.
Lallana has yet to feature for either Liverpool or England so far this campaign due to the problem, but he is expected to be a shoe-in for Gareth Southgate's World Cup squad should he return to full fitness and get a run of games under his belt.
Speaking ahead of Liverpool's Champions League game against Maribor manager Jurgen Klopp was delighted by the news, telling the club's official website: "It's absolutely good news. I cannot say now, but maybe after the next international break he could be back.
"It would be fantastic for us, of course. Everybody knows what kind of a quality player he is, so it would be fantastic. We don't have to think about this. I cannot now mention it if I need it and then when I don't need it then I say it's not important. It is like it is.
"Of course, it's better if Adam could have scored in one game or another, but there is nothing we can do about this. It's just good that he's back in a few weeks."
During his spell in Qatar, Lallana bumped into former Barcelona star Xavi and took to Instagram to let his followers know about the chance encounter,
"Great week stepping up the rehab even further - getting stronger each and every day," he posted on the social media platform.
"Added bonus of meeting and chatting to one of my idols as well - Xavi. So down to earth despite being one of the greatest players of his generation."