The striker has been linked with a £40 million move to Real Madrid.
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Luis Suarez has three weeks to sort out his future or face staying at the club for at least another season, the Daily Mirror reports.
Suarez future has been the subject of intense speculation since the end of last season, with rumours stating that the Uruguayan has already agreed personal terms with Spanish giants Real Madrid.
Liverpool want the strikers future sorted out by the end of the month or he will be expected to join up with the Reds squad for their pre season tour of the Far East and Australia.
No offers have been received for Suarez despite the speculation surrounding a move to Real Madrid and even though the striker has spent most of the past month flirting with Madrid through the media, it is thought that Los Blancos are reluctant to pay the £40 million asking price that Liverpool are demanding.
The Reds don’t need to sell the striker as he still has three years left on his contract and Liverpool manager Brendan Rodgers is starting to get fed up with the constant speculation surrounding Suarez.
If Suarez does want to force though a move away from Liverpool, he may have to come back to Anfield from his holiday and ask for a transfer himself.