Suarez: It would be difficult to say no to Real
Suarez received a 10-match domestic ban for biting Chelsea's Branislav Ivanovic last month and suggested the pressure from the British media was one reason why he would consider a move.
"There is nothing concrete but it will always be difficult to say no to Real Madrid," the forward, who is in Montevideo with the Uruguay squad, told local radio station Radio Sport 890.
"I love Liverpool, but if there's any chance to play elsewhere? I've suffered a lot from when I was a kid for some English journalists to be criticising me in an unfair manner only for my attitudes and not as a player."
The 26-year-old has had a chequered disciplinary record in England and was fined and suspended during the 2011/12 season for racially abusing Manchester United's Patrice Evra.
Suarez, who was also banned for biting an opponent when he played for Dutch side Ajax, was Liverpool's leading goal-scorer last season, second only to Manchester United's Robin van Persie in the Premier League with 23 goals.