Flanagan returned from a lengthy spell on the sidelines in January.
Flanagan's current deal expires in the summer and the defender only returned from a 20-month spell on the sidelines with a persistent knee injury in January.
He has remained a popular member of the squad among the fanbase, who are keen to see some local talent maintain that connection between the side and the supporters.
The report also says that manager Jurgen Klopp has been delighted with the attitude of Flangan since his return to the fold, with Klopp recently expressing regret for omitting the 23-year-old from Liverpool's Europa League squad for the second half of the campaign.
By keeping hold of the player, he provides cover for both flanks in the full-back positions having played on the left side prior to his injury problems in the 2013/14 season. Since his return he has been operating on the right-side and it looks as though he will continue to compete for a place there given regular right-back Nathaniel Clyne operated on the left side in order to accommodate Flanagan's place in the side in a recent 3-0 win over Manchester City.
One would think he is likely to get a few more opportunities between now and the end of the season, while next season he will look to force his way into the side and hold down a regular place once more.