The Uruguayan's future is already one of the sagas of the summer, with the controversial 26-year-old striker having made a number of statements pertaining to his unhappiness at life in England and also about the direction he sees his career taking.
The former Ajax forward is currently midway through another lengthy suspension – 10 games ban for biting Chelsea's Branislav Ivanovic during a English Premier League game towards the end of last season – and has spoken openly about his desire to play for Real Madrid.
He has cited press victimisation as one of the factors behind his thinking, saying the English media judge him on matters other than football ability, and the South American appears keen to manufacturer a move away.
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 misdemeanours ranging from being found guilty by the English Football Association of racially abusing Manchester United's Patrice Evra, to a perennial debate about diving and finally his biting of Ivanovic.
Liverpool fans have stuck by him throughout, recognising his brilliance as a player, and he conceded he will always appreciate their support.
"The love I have for Liverpool I will never forget," said Suarez, who is away with Uruguay in Brazil for the Confederations Cup.
"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."
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