Suarez has been linked with French outfit Paris St Germain, a move which would bring a premature end to his tumultuous time in England following his transfer from Ajax in January 2011.
The Uruguayan has become a hate figure for rival fans after he was fined and banned for eight games earlier this season for racially abusing Manchester United's Patrice Evra in a league match in October.
Yet he has reject the prospect of leaving Anfield before his contract expires in four years' time - and even admits his thoughts have already drifted towards securing an extended deal.
"I want to stay. Despite everything that happened, I am very happy here, on and off the pitch," Suarez told Uruguayan website ovaciondigital.com.
"Liverpool is one of the biggest clubs in Europe, with a history. As a child I saw them play and loved it. And the club are happy with me and want me to stay.
"I have a contract until 2016 and already want to renew.
"The manager remains confident in me and that is very important, especially after being out for eight games."
Suarez compounded his racism charge by refusing to shake Evra's hand before Liverpool's 2-1 defeat to United at Old Trafford on February 11, and the 25-year-old admits he still harbours a sense of injustice over his treatment at the hands of the Football Association.
"In the case of suspension of eight games I think I was a victim," he said.
"What hurts me most is that I was in court and there was no concrete evidence. It was just my word against another player and they believed him. That hurt a lot.
"I do not think I deserve to be treated like I was treated."
Despite banging in the goals during his time in Holland, Suarez first came to wider attention at the 2010 World Cup when his deliberate handball on the goal-line against Ghana ultimately was pivotal in Uruguay booking their place in the semi-finals at the expense of the African nation.
It was an action for which Suarez was widely pilloried, but he says both that incident and his clash with Evra are moments that he refuses to dwell on.
"Obviously, if you read on the internet and newspapers, you think I'm going through something very difficult, but the truth is that I'm fine," he said.
"It's similar to what happened with my hand in the World Cup. But these things happen in football. Some day they will be anecdotes and I try to forget them today."