The bid was made on Tuesday after Liverpool had turned down a previous offer of £30 million, sources told ESPN. It is understood that Arsenal have made their latest bid in the belief that it will trigger a reported £40 million release clause in the contract Suarez signed last summer.
But Liverpool have knocked back the new offer, maintaining that they are only compelled to inform the 26-year-old of any bids exceeding that amount – and that they do not have to sell at that price.
They have made it clear that they do not want to sell the striker, and are unlikely to contemplate any offers below £50 million.
Suarez is scheduled to hold talks regarding his future with Liverpool manager Brendan Rodgers in Australia on Wednesday, following a friendly against Melbourne Victory at the MCG.
Arsenal manager Arsene Wenger’s desire to sign the Uruguay international has intensified after being frustrated in his attempts to sign Real Madrid forward Gonzalo Higuain, who looks set to join former Liverpool manager Rafa Benitez at Napoli.
But Liverpool manager Brendan Rodgers said on Monday that he expects Suarez to honour his contract, which has three years to run.
Rodgers has also stated that he believes the striker to be as valuable as Edinson Cavani, who recently joined Paris Saint-Germain for £55 million on June 16.
Suarez, signed from Ajax for £22.8 million in January 2011, first announced in May that he wanted to leave Anfield.
He initially claimed he was been driven out of the Premier League by the British media and the Football Association, having been given a 10-match domestic ban for biting Chelsea defender Branislav Ivanovic during a Premier League match at Anfield on April 21.
He then said earlier this month that he was flattered by Arsenal’s interest, with his agent Pere Guardiola indicating to Liverpool that the forward wanted to join a club in the Champions League.
Suarez flew to Melbourne on Sunday to join up with Liverpool’s pre-season tour of the Far East and Australia, having been given a break by the club after playing for Uruguay at the Confederations Cup in Brazil in June.
The striker has six games still to serve on his domestic ban for biting Ivanovic, and will not be able to play in the Premier League until September.