The centre-back did not feature in last night's Champions League play-off against Braga in Portugal, with sporting director Ramon Rodriguez confirming the 30-year-old had been asked to be left out so as not to be cup-tied after hearing of Arsenal's offer.
Sevilla are believed to want around £6.5million for the former Lyon centre-back, part of Les Bleus' ill-fated World Cup squad in South Africa, but it would appear the Gunners have not yet matched that valuation.
Another stumbling block to completing any deal is likely to be the length of contract, with Arsenal usually only offering one-year contracts to senior players, although that was waived when veteran Mikael Silvestre signed from Manchester United in 2008.
Sevilla are understood to have called an emergency board meeting as they discus the offer, which could hinge on whether they can bring in a replacement before the transfer window closes on September 1.
"The player asked not to play because of the offer from such a big team, but, for the moment, we believe the offer is insufficient and Squillaci is still a Sevilla player," said Rodriguez.
Arsenal are certainly in need of cover in the centre of defence, with Silvestre, William Gallas and Sol Campbell all leaving at the end of their contracts, while Philippe Senderos completed a permanent move to Fulham.
Wenger has already invested in a new defender this summer, signing promising centre-back Laurent Koscielny in a £10million deal from Lorient.
The 24-year-old had an eventful Barclays Premier League debut at Anfield, being the subject of a late challenge from Joe Cole which earned the new Liverpool midfielder a straight red, before later receiving his marching orders following two yellow cards which rules him out of Saturday's home game against Blackpool.
Any deal for Squillaci, though, appears unlikely to be pushed through in time for him to play at the weekend, while left-back Armand Traore looks set to be leaving for Benfica after falling behind new England international Kieran Gibbs in the pecking order at Emirates Stadium.
The Gunners will be without Samir Nasri for at least a month after the winger underwent minor knee surgery, and reports in Italy suggest Wenger could now rekindle his interest in Fiorentina's £18million-rated midfielder Riccardo Montolivo.