Suárez's agent, Pere Guardiola, reportedly formulated a figure, believing a bid in excess of £40m would allow his client to leave Anfield.
Liverpool's managing director Ian Ayre told Arsenal chief executive Ivan Gazidis over a fortnight ago £40m would not be enough to persuade the Anfield club to sell their terrific, but temperamental, striker.
The Gunners had a £30m offer turned down 17 days ago for Suárez, who has since said he was flattered by last season's fourth-placed team's interest.
Liverpool owner John W Henry mocked Arsenal's extraordinary bid, tweeting, "What do you think they're smoking over there at Emirates?" referring to Arsenal's stadium name.
What do you think they're smoking over there at Emirates?— John W. Henry (@John_W_Henry) July 24, 2013
Tabling such a high fee is uncharacteristic of Arsenal, mocked by their own fans in recent years for their prudence in the transfer window.
Andrei Arshavin remains the club's record signing at £15m, but the club's eight-year trophy drought has compelled the board to free around £70m worth of funds for manager Arsène Wenger to reinforce an underachieving squad.
Wenger must now decide whether to return with a bigger offer for 26-year-old Suárez, currently in Melbourne on Liverpool's pre-season tour.
Arsenal have shown tangible interest in Suárez, Gonzalo Higuaín and Wayne Rooney this summer, and it would be embarrassing for the club should they fail to sign one of the three forwards.
Though Suárez would bolster a forward line littered with unconvincing strikers, a goalkeeper, a centre-back, a defensive midfielder and a winger are other areas Arsenal need to strengthen.