The right-back has been struggling with a knee injury.
Flanagan missed the back end of the Reds' pre-season tour of the United States with a knee injury and has missed the start of the season as a result.
The 21-year-old's return could be handy for manager Brendan Rodgers given injuries picked up during Monday night's defeat against Manchester City. Glen Johnson seemingly pulled up with a thigh injury and Alberto Moreno seemed to strain his ankle - though the latter managed to finish the game at the Etihad Stadium.
Flanagan told the Liverpool Echo: “I’ve been struggling with fluid in my left knee.
“I just felt it during the tour and it’s been a bit inflamed.
“It’s just something we have to be careful with.
“I want to be back out there but I can’t rush it. I need to make sure that when I do come back I’m 100%.
“I don’t think I’ll be back for this weekend but I’m hoping to be fit for the Villa game.
“The next couple of weeks should give me the chance to get back into full training and build up my fitness.”
If Flanagan is fit in time for the visit of Aston Villa, he'll join up with the team at a time when the Reds' fixture schedule gets that little more hectic given their participation in the Champions League.
With two full-backs also struggling with injury, Rodgers will delighted to have another player at his disposal as the side adapts and gets used to playing two to three games a week.