The Uruguay international, who has also refused to rule out a move to Real Madrid, believes he has been harshly treated since moving to the Premier League from Ajax in January 2011.
Suarez, who admits his love for Liverpool is not enough to make him want to stay at Anfield, compared his eight-game ban for racially abusing Manchester United defender Patrice Evra to John Terry's more lenient punishment for a similar offence, and believes he has been unfairly singled out.
|4/7||Luis Suarez is 4/7 with Paddy Power to join Real Madrid
"Liverpool is a club that I dreamt about playing for as a boy. I have been with great players there, they know me and I would love to continue for many more years at Liverpool. The stadium is spectacular, the fans are phenomenal: people with tattoos of me, things that I could never have imagined.
"After the [Evra] suspension people would come up to me, this is something that really touched me and they would say: "Luis forget everything and stay."
"But I can't forget as it was something that I had to suffer, that my family had to suffer and away from football I have a family to support and who are hurt by these things."
Suarez is currently serving a 10-game ban for biting Branislav Ivanovic and says that the stigma now attached to him is affecting his private life and the happiness of his family.
"About a week ago I was walking in a shopping centre near Manchester and three or four guys asked me for a photo," he added.
"While we were posing for it my wife said to me "Luis, get out of the photo". She noticed they were making biting gestures. I was with my wife and my daughter. Things like that get on your nerves. My wife was on the brink of tears and the blokes ran off laughing. You get tired of stuff like that."