The Uruguay international has been in great form for Brendan Rodgers' side this season despite the team's domestic struggles, finding the net 11 times in the Premier League and dazzling fans with impressive attacking play.
And despite the Merseyside club being five points off of the top four going in to Christmas, the 25-year-old striker wants to achieve "big things" at Anfield, starting with qualifying for Europe's top club competition.
"My dream and desire is to play in the Champions League and achieve big things with Liverpool, because they're the club I wanted to play for, and now that I'm here, I want to stay for a long time," Suarez told The Daily Mail.
|6/1||Liverpool are 6/1 with William Hill to secure a top-four spot in the Premier League this season
"Just like I waited to play in the Champions League with Ajax and I had that chance, now I hope the same thing happens with Liverpool.
"All I can say is that my head is here now and for many years to come."
The Liverpool forward has had a number of controversial moments during his time in England, and has been repeatedly criticised for going to ground too easily, although he argues it is merely a reflex reaction in a physical league.
He explained: "Sometimes you're standing there and someone comes flying in, so you move your leg out of the way or you go to ground because you’re scared of getting hit.
"If I leave my leg there so the referee can see it’s a foul, I risk suffering a big injury. That’s why sometimes your instinct tells you to go to ground.
"It's a split-second instinct, not a conscious decision you make on the pitch. Of course, I don't want people to go around saying 'this guy just dives'."
However, Suarez also suggests he is attempting to mend his ways in terms of diving in order to become a more successful player in the Premier League.
"I'm trying to change and to avoid [diving] because I know that football is different here, and it's helping me at the same time," he added.
Brendan Rodgers' side picked up an emphatic 4-0 win over Fulham at Anfield on Saturday to put themselves eighth in the table, and travel to Stoke on Boxing Day.