Suarez open to Real switch
Suarez, 26, is contracted to the English Premier League side until 2016, but has been the subject of speculation linking him with a move away from Anfield since receiving a 10-match ban for biting Chelsea defender Branislav Ivanovic.
With Gonzalo Higuain looking set to exit the Santiago Bernabeu, Real have been linked with moves for the Uruguayan pair of Suarez and Edinson Cavani.
Suarez said there had been no formal offers for his services, but admitted a potential move to Real Madrid interested him.
"I've talked to my agent – there's nothing concrete. To say no to Madrid would always be difficult and more so with the team they have," Suarez told Uruguayan radio station Sport 890.
"I have a contract with Liverpool, but it would be very difficult to say no to Real Madrid. There are a lot of rumours in the transfer period, but you never know until firm offers are made.
"I've talked to the coach (Brendan Rodgers), and he knows what I want. He was a player. Some of the players understand my situation – enough said."
Biting Ivanovic only added to a long list of misdemeanours Suarez has committed during his time in England.
Suarez said he loved Liverpool but is unhappy with the way he has been treated by the English press.
"I love Liverpool, but if there is a chance of playing somewhere else … I suffered too much as a kid to get where I am to be attacked unfairly by the English press," he said.
"They haven't appreciated me as a player. They've just judged my attitude.
"I'm happy at Liverpool, I'm happy because of the fans. I made a mistake, I'm human, but (the press) talked about me in ways they shouldn't have.
"My family have suffered and things got out of hand. My daughter and my wife have suffered. I'm not prepared to continue to put up with the English press."
Suarez has developed into one of Europe's best goalscorers since joining Liverpool from Eredivisie giants Ajax in 2011.
He is set to miss the first six games of the 2013/14 season after his suspension for biting.