Arsenal will have to increase their £30m offer if they are to pull off the shock transfer of the summer and land Luis Suarez.
The bid for the Uruguayan forward was made at the end of last week and Liverpool's initial reaction has been to dismiss it out of hand.
They denied claims last year that Suarez had a £40m buy-out clause in the contract he signed when he moved from Ajax in 2011. However, Marca claimed last month that the player has a €47 million clause in his contract that would trigger a sale.
Suarez is not due back at Anfield until July 22 after being given additional time off because of his involvement in the Confederations Cup.
The 26-year-old has admitted during the summer that he wants to leave England because he feels victimised. He still has six games of a 10-match suspension to serve for biting the Chelsea defender Branislav Ivanovic last season.
Suarez has also spoken of his desire to move to Real Madrid. He said: "To say no to Madrid would always be difficult and more so with the team they have. 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 [Rodgers], and he knows what I want. He was a player."
Suarez still has three years left on his contract at Anfield, but his future now remains in huge doubt in light of Arsenal's bid to land the player, which could yet draw a reaction from Real Madrid.
Arsenal have also put together a £22m package to land the Madrid striker Gonzalo Higuain.