Liverpool striker Luis Suarez wants to hold talks with Arsenal over a potential move to the London club.
Suarez believes Arsenal's offer of just over £40m - which was rejected - triggered a clause in his contract that allows him to speak to suitors.
Liverpool interpret the clause differently, but the 26-year-old will inform Reds boss Brendan Rodgers of his wish to meet with Arsenal.
The Anfield side have now turned down two offers from the Gunners.
But with Real Madrid forward Gonzalo Higuain, another of their targets, reportedly set to complete a move to Napoli, Arsenal will put all of their efforts into signing Suarez.
Suarez in numbers
30 goals in 44 appearances for Liverpool last season
Since joining from Ajax in January 2011 for £22.7m, has scored 51 in 96 appearances
49 goals in 48 games for Ajax the season before joining Liverpool
31 goals in 62 appearances for Uruguay
Following Arsenal's most recent approach, a post on Liverpool owner John Henry's Twitter page read: "What do you think they're smoking over there at Emirates?"
It is unclear whether Henry is talking about Arsenal's attempts to sign Suarez or their valuation of the player.
The Gunners' unusual bid of £40,000,001 was designed to trigger the clause in the player's contract that stipulates Liverpool must consider any offer in excess of £40m and give Suarez the option of talking to the club - but the Reds do not have to sell.
While Liverpool remain determined to keep their prized asset, who scored 30 goals for the club in 44 appearances last season, their resolve is likely to be tested if the bidding continues to rise.
Real Madrid remain interested in the Uruguayan but have yet to make a formal offer.
Arsenal are waiting to learn the outcome of the striker's meeting with Rodgers on Liverpool's pre-season tour to Australia before deciding how to proceed.
Suarez could make his first appearance for the Reds this summer on Wednesday, after being named among the substitutes for the friendly against Melbourne Victory.
Should Arsenal persist and have an improved bid accepted, it could come close to trebling their previous highest initial outlay on a transfer.
Arsenal's record buys
Jose Antonio Reyes (Seville) £17.5m
Santi Cazorla (Malaga) £16m
Andrey Arshavin (Zenit St Petersburg) £15m
Sylvain Wiltord (Bordeaux) £13m
Thierry Henry (Juventus) £11m
The Gunners, whose first offer for Suarez was £30m, paid a reported £15m to Zenit St Petersburg for Andrey Arshavin, in January 2009.
Rodgers last week said he considered Suarez to be at least as valuable as Edinson Cavani, who recently joined Paris St-Germain for £55m.
Suarez joined Liverpool in Australia at the weekend after flying to Melbourne from Montevideo on Sunday, having been given extended leave by the Reds following the Confederations Cup.
He wants to leave Anfield to play for a Champions League club despite only signing a new long-term deal last summer.
Speculation has grown about Suarez's future since he was punished with a 10-game ban at the end of April for biting Chelsea's Branislav Ivanovic.
The striker still has to serve six games of that suspension and was also banned in 2011 after being found guilty of racially abusing Manchester United's Patrice Evra.
Suarez joined Liverpool from Ajax in January 2011 in a £22.7m deal.
I'd say he disgusts me but that wouldn't be adequate if this is correct. What an absolute joke of a person.