The Uruguay international has said that he would like to leave the Reds after insisting that he has become disillusioned with life in England.
Arsenal, Chelsea and Real Madrid have all been linked with a move, but Liverpool are reluctant to let their star man leave. However, the 26-year-old is hoping to push a move through in a bid to further his career.
"If I receive an important offer to progress my career, I will study it," Sky Sports News quotes Suarez as saying. "Some clubs have asked about me but I hand questions over to my agent. I am no stranger to rumours.
"I always want to improve. That's why I left Ajax for Liverpool. But this club needs to fight to enter the Champions League and, when it doesn't happen, it damages the morale of any player. So I've suffered. It is hard to view the Premier League every week with never a chance of winning it.
"On top of that, the English media do not understand me. The controversies with [Patrice] Evra and [Branislav] Ivanovic were decisive. There are always extra questions when people analyse me. Had that not happened, perhaps I would have been regarded as the best Premier League player last season."
Suarez joined Liverpool in 2011 from Ajax.