Flanagan's current deal runs out in the summer.
Flanagan's current deal runs out at the end of the season, and returned from a persistent knee injury after 20 months on the sidelines in January.
Henderson is quoted in the Liverpool Echo, saying: "I don't think players and people like Flanno grow on trees to be honest.
"You have people like him and Stevie and Carra who have come through the Academy. The fans feel as though they are one of them really which they are.
"His whole family supports Liverpool. He has been a Liverpool supporter since he was a kid and he has had a difficult time for the last two years, but what I have seen him do behind the scenes is incredible really.
"He is a huge player for us, a huge player for the club and the fans as well. It is in everyone's interests for that to be sorted out soon."
Given that he has only just returned from injury, it's of little surprise that he hasn't had regular game time, but one thing Flanagan does possess is that connection between the fanbase and the players on the pitch - something which you'd think manager Jurgen Klopp will want to exploit as much as possible. It's something that hasn't really been there since the departures of Steven Gerrard, and Jamie Carragher before him.
Then there's the current predicament with Liverpool's full-backs. Nathaniel Clyne has been a solid performer but there is a lot of concern with the performances of Alberto Moreno. After those two members of the squad, resources are a little thin on the ground - and there is surely an opening on the left flank where Flanagan has operated in the past.
One thing Flanagan offers if nothing else is bite, something which this side has been sorely lacking - some feel Liverpool are too nice to play against at times, that wouldn't be the case with a player in the mould of the 23-year-old playing at the club on a more regular basis.
Liverpool have a track record of letting younger players contracts run down, but this is one they perhaps need to sort out very quickly. It's caused enough concern that the captain has had his say.