The Uruguayan striker's future is already one of the sagas of the summer, with the controversial 26-year-old having made a number of statements about where he sees his career going.
He has cited press victimisation as one of the factors behind his thinking and appears keen to move, and added further to that today.
Speaking to Marca he said: "First I have a contract with the club, but if one day I want to sign (for another club), Liverpool will hear the offer, as it does with other players.
"They must agree with other teams, but the word of the player, in this case mine, is important. If you need a change, you should listen to the player.
"Every player aspires (to be the best) and if you ask a child of eight years they would say one day they would go to Real Madrid or Barcelona."
Suarez has been a divisive figure during his time at Liverpool, with misdemeanors ranging from his racial abuse of Manchester United's Patric Evra, to a perennial debate about diving and finally his biting of Ivanovic.
Liverpool's fans have stuck by him throughout, recognising his brilliance as a player, and he admits that he will always appreciate their support.
"The love I have for Liverpool I will never forget," he added.
"I love the city, the club and the people and everyone is welcome. All I ask is for respect for all the things that have been said."
Suarez has also conceded that some of his critics may be right in condemning his on-field theatrics.
"There are moments of importance (in games) and I have lived football in a very particular way since childhood," he said.
"But I know I can play tricks. Sometimes I protest too much to the referee. I have to take it a bit better."
- Sports & Recreation
- Branislav Ivanovic
- Real Madrid