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The former Sunderland player is expected to sign the new contract this week, ending months of talks.
The England international joined Liverpool from the Black Cats in 2011 in a deal worth around £20m.
With Steven Gerrard leaving at the end of the season for Major League Soccer side LA Galaxy, the 24-year-old is among the favourites for the captaincy.
Vice-captain Henderson, whose current contract expires at the end of next season, has scored seven times in 55 games for club and country this campaign.
Liverpool midfielder Jordan Henderson is close to agreeing a new £100,000-a-week, five-year deal with the club.