The Hungary midfielder has been linked with Real Madrid in recent weeks.
But he told the Liverpool Echo on Friday: "I love being here.
"My family is happy, I love the club, I love the fans, I love to play for this club and that is it."
On being likened to Reds legend Steven Gerrard, Szoboszlai also said at the Football for Change Easter event: "It is a big compliment.
"But I've many times that I just try to do my own story and sometimes we struggle as a team but we always try to put everything on the pitch and then this season I do stuff off the pitch, trying to help the new guys, coming from different leagues.
"I know how it feels to be new and I know how hard it is to come to the Premier League and especially Liverpool where you are always expected to win trophies.
"I hope (I am becoming a leader) but you have to ask someone else how they see it but I try to do my best on and off the pitch, try to keep everyone (together), try to be a leader (with) what I am doing on the pitch and that is the most important thing for me. Hopefully we can change this season in a good way."