The Uruguay forward, who has been fiercely criticised by the English media for his bizarre on-field antics including biting opponents, has been linked with Real Madrid, reports Xinhua.
"Liverpool has treated me very well and I only have words of thanks for the fans, but I'm not prepared to keep putting up with everything the British press says," Suarez said. "I love Liverpool and everyone knows I have a contract, but if there's a chance of playing elsewhere I'd think about it."
Suarez admitted that there was "nothing concrete" about a move, but added "it would be difficult to say no to Real Madrid".
Suarez had been suspended for eight games in December 2011 for making racist remarks toward Manchester United defender Patrice Evra during a match. He was suspended 10 matches for biting an opponent in April.
"I know I've made mistakes and when I have I've apologized, but the press has dedicated itself to talking about me as if they've known me all my life, saying things that have nothing to do with football," Suarez said.