The Uruguay striker looks set to leave Liverpool after claiming that what he perceives as unfair treatment from the FA and the English media outweighs his love for the club.
The 26-year-old is yet to hand in an official transfer request, but has told Spanish newspaper Marca: "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 claimed manager Brendan Rodgers knew about his desire to leave but Liverpool seemed to deny that in a statement last month. Liverpool said they expected the striker to honour his contract, which has four years left to run.
Suarez has six matches of a 10-match domestic ban still to serve for biting Chelsea's Branislav Ivanovic in April, and was also banned for racially abusing Manchester United's Patrice Evra and Suarez has conceded that his critics may be correct in condemning him for his behaviour.
"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.
"There are moments of importance (in games) and I have lived football in a very particular way since childhood.
"But I know I can play tricks" he added.
"Sometimes I protest too much to the referee. I have to take it a bit better."
It is reported that Real Madrid are keen to sign Suarez, but a bid is unlikely to come in before a manger is in place at the Spanish league runners up.
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