The Uruguay international, who has been unsettled at Anfield and blamed referees and the media for that, has been open about his unhappiness of living and playing in England.
"I will give my soul every time I step on the pitch," Suarez told El Pais. "I have done this with Uruguay, Ajax and Liverpool. I do not hold anything when I finish a game.
"A player always aspires to be at the top of their profession and Madrid is at the top for any football player.
Suarez also spoke of his desire to play in the Uefa Champions League, which Liverpool have failed to qualify for.
"It disturbs me that Liverpool are not in the Champions League every season.
"I've suffered at Liverpool, but when I think of what it represents to play for this club, and the love my daughter has – she sings the hymn – the hairs on the back of my neck stand up when I play at Anfield," he however said.
The 26 year old, who has not submitted an official request yet, has been a controversial figure on the pitch in the English Premier League.
Still to serve six matches of a 10-match ban for biting Chelsea's Branislav Ivanovic in April, he had earlier been suspended for racially abusing Patrice Evra, the Manchester United defender.
"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," Suarez was earlier quoted as telling Spanish newspaper Marca.
"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, who signed a new contract last summer, has four years of his current deal left to run.
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