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."