Unai Emery had looked nailed on to snare the exciting youngster last week.
But their arch rivals Tottenham entered the fray and tabled a higher offer, thought to be in the region of £27m.
The Gunners are now back on top and look set to implement their original plan, though.
Saliba is not deemed ready for Premier League football by Emery and will be sent back to Saint-Etienne on loan.
READ MORE: Man Utd agree £80m Harry Maguire transfer
“William Saliba is heading to Arsenal”
But with Arsenal only having limited funds this summer, former star Perry Groves is raging.
“They’re in for William Saliba,” he told talkSPORT.
“He’s £26m and they’ll loan him back. They’re not in a position to do that.
“I want all of the budget going on players now that will make an impact.”
Emery still has a big call to make on Laurent Koscielny.
The France international, who is angling for a transfer, refused to join the rest of the Gunners squad on their pre-season tour of the USA.
The 33-year-old is being tracked by French sides Bordeaux and Lyon.
Koscielny was club captain, but Emery admitted he’ll now need to mix things up.
“I want one English player in these five captains,” he said. “Last year [Granit] Xhaka, Mesut [Ozil] and Nacho [Monreal] were working as captains.
“But after Aaron Ramsey and Petr Cech left – and possibly Laurent Koscielny – I will want more.
“An English player who grew up in our academy can understand the English spirit and Arsenal values. These are the qualities and more [we want].
“We lost some players with big experience and a long time in England and Arsenal like Cech and Ramsey. We lost Koscielny too. They started one day being captain when they were young.
“We have young players with experience, players starting for the first time to be considered as captains. If we decide on a player they have the capacity and deserve to have the opportunity to be captain.
“(I look for) experience of leadership, being an example on and off the pitch, character and communication with the coach and other players, capacity to speak and to be there for supporters, a good connection and communication with the club.”