The former Sunderland man has struggled for game time since the arrival of Brendan Rodgers, with plenty speculation circulating that he could be on the move from Anfield.
Henderson was understood to be one of the players offered to Fulham in the summer, as Liverpool failed in their attempts to sign American forward Clint Dempsey.
But the England midfielder still sees his long-term future on Merseyside and is keen to show he can be a regular Liverpool player, despite the recent arrival of Joe Allen.
The 22-year-old told Sky Sports: "I love playing for Liverpool, it is a real passion of mine. When I put the shirt on it is a real honour to go out and play for Liverpool, so I want to do that for the rest of my career.
"I will keep fighting and I have belief in my own ability that I can be a success here. I have got a good relationship with the manger, I think everybody has, and I feel he has improved my game since he came to the club."