The England international initially struggled to show his best form on Merseyside when he joined from Sunderland in June 2011.
However, the midfielder has become a pivotal figure in Brendan Rodgers' first team and looks certain to take over as captain from Steven Gerrard when he leaves for LA Galaxy at the end of the season.
And Henderson wants to be a main man at Anfield for years to come.
"It's definitely not [a major issue]," he said. "I love playing football for Liverpool and I want to be there for many years.
"In terms of my contract, I think everybody else will make a big deal of it but for me it's just letting my agent and the club deal with it and whenever it gets sorted, it gets sorted. All I want to do is my best for club and country."
With Gerrard set to end his lengthy association with Liverpool, Henderson has been tipped to fill the talismanic skipper's boots.
Henderson is unfazed by that prospect, though, and says he has learnt a lot from the former England captain.
"When I first came to the club, he was brilliant with me. When I wasn't playing so much, he was just the same, helping me on the field with what I needed to do and improve on," he added.
"And also off the field, he's brilliant. He's just got this sort of presence about him, that real leadership. He's just a real humble person as well, which is amazing really, for all the young players at Liverpool.
"I'm sure everybody there has learnt a lot from him."
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