The former Sunderland player, who was linked with a summer move away from Anfield, has started every Premier League game for the Reds in the 2013-14 campaign so far.
"He told me that he wanted to stay here and fight," Rodgers told the club's official website.
"I told him I would help him improve as a player and improve his game because he has got all the tools.
"At 23 years of age, he has got his whole career in front of him. It is thanks to his quality and professionalism that he is making marked improvements."
Henderson's recent form has earned him a spot in the England squad for upcoming friendlies against Chile and Germany.