While practicing with the Uruguay national team, Suarez takes time out to once again criticise his treatment in England by the press and public.
Luis Suarez says nationality is part of his problem in Premier League
"Every player wants to reach the top and Real Madrid are one of the top clubs," he told a Uruguayan television programme.
"But everything that has been said so far is just speculation, I haven't received any concrete offers."
Suarez has revealed before that he is not happy with life in the Premier League, where he feels he has been chastised by the media for his conduct, and aired his complaints once again.
"The press have made me feel bad since the moment I arrived in England," he said. "They have never judged me on how I play football, they judged me on my attitude."
He blamed his public perception for not being chosen as the PFA Player of the Year.
"They said I dived, moaned, postured, they said I was racist, they said everything," Suarez said. "They have never spoken well of me. That's why, when people said that I could have been chosen as the best player in the Premier League, I said, 'I'm relaxed, I know that in England I'm never going to be given an important prize'."
Although Suarez emphasised he enjoys playing for Liverpool and was grateful for the support he has received at Anfield, he admitted his love for the club and its supporters may not be enough to convince him to stay.
"After the suspension, the fans all supported me," he said.
"That's something I remember and it has made me think, 'Luis, forget it all and stay'. But I cannot forget it, because I have suffered, my family have suffered, and away from football, I have a family that supports me, and these things hurt them."
The Uruguay striker also believes his nationality plays a part in his persona, pointing to the eight-match ban he received in 2011 for racially abusing Patrice Evra, compared with the four-game ban given to John Terry for a similar spat with Anton Ferdinand.
"I'm South American and I think that's the root of all of this," he said.
The FA declined to comment when contacted about Suarez's comments.
Meanwhile, Manchester United have completed the signing of Uruguayan right-back Guillermo Varela on a five-year contract.
Varela, 20, moves over from Penarol.
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