Luis Suarez will be allowed to hold talks with Arsenal but Liverpool have no intention of selling their striker until his £50m-plus valuation is met, the BBC reports.
Arsenal's club-record bid of £40m plus £1 was firmly rejected by Liverpool but Suarez now wants to hold talks with the north London club.
The approach triggered a clause in his contract that means he has been told of the bid and can now talk to Arsenal.
But Liverpool will not sell him until Arsenal up their offer significantly.
With Liverpool 1-0 up, the Uruguayan laid on the Reds second for new signing Iago Aspas late in the match.
After the game Liverpool manager Brendan Rodgers said: "There's nothing new to report, he [Suarez] is very much a Liverpool player and over the course of the next couple of weeks we've got to get him up to speed."
Rodgers did, however, remind Suarez of the debt he feels the player owes the Liverpool fans who have stood by him after two seasons of controversy.