The full-back, who picked up the injury during the Reds' pre-season tour of the USA, could be sidelined for up to three months.
"He'll probably be out for up to three months. He's had his knee cleared out. The initial thinking was six weeks or so but it's going to take a bit longer," The Mirror quotes Reds boss Brendan Rodgers as saying.
Meanwhile, Flanagan's fellow Liverpool full-back Glen Johnson has resumed training and could return to the squad to take on Everton in next weekend's Merseyside derby.
Martin Skrtel is expected to return to the starting XI against West Ham United this weekend.