Suarez is being linked with a £50 million move to Manchester City in January.
But he told liverpoolfc.com: "I have a very long contract here and it's a dream come true to be playing at a club like Liverpool because, as I've said, as a boy I dreamt of playing for a team like this.
"Now I'm here it's all about enjoying myself and trying to be here for as many years as I can, because I'm at a club where I'm very happy, my family is happy, I've got fantastic team-mates and a manager from whom I'm learning so much.
"As a player, it's vital to have the backing of your manager and so I think that the confidence Brendan is showing in myself and the team as a whole is very important and it's down to us to repay that trust out there on the pitch.
"Let's hope we can keep improving. I'm working well and I'm very happy at a club where I've always wanted to be. At a club to whom I'm very grateful for the trust everyone is showing in me, a club with amazing supporters and team-mates who are all great people.
"The other important thing is that the squad is very united. In spite of not getting the results we would have liked, we have a great spirit of togetherness and let's hope we can continue to pick up points."