The Sun says Flanagan may be on the move in the new year.
The full-back, 24, is out of contract at the end of the campaign but could leave Anfield sooner if a Prem club comes in.
Flanagan was loaned to Burnley last term and the Clarets might try for another loan.
But it is more likely that a full-time move sees the loyal servant pack his bags.
Injuries slowed Flanagan's progress but his attitude has always been spot on.