Squillaci, 30, asked to be left out of Sevilla's Champions League play-off against Braga last night to avoid being cup-tied.
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A statement on the Sevilla website read: "Sebastien Squillaci's future is in the air.
"As was confirmed by sporting director Ramon Rodriguez at the airport in Porto, the club have received an offer from Arsenal.
"The player asked coaches not to play him in the match."
Arsenal have already invested in the defence this summer, signing promising centre-back Laurent Koscielny in a £10 million deal from Lorient.
Koscielny had an eventful Premier League debut at Anfield, being the subject of a late challenge from Joe Cole which earned the new Liverpool midfielder a straight red card, 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.
"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, quoted in Spanish newspaper Marca, following the 1-0 defeat in Portugal.
Sevilla are said to have called an emergency board meeting today, as they discus the offer, which could hinge on whether they can bring in a replacement before the transfer window closes on Sept 1.
Arsenal are also said to be keen to sign an experienced defender, linked with both Australian stopper Mark Schwarzer and Republic of Ireland international Shay Given.
Full-back Armand Traore, meanwhile, looks set to be leaving for Benfica.
The 20-year-old signed from Monaco in 2006 but has not been able to break into the Arsenal first team on a regular basis and spent a season's loan at Portsmouth.
With the emergence of England international Kieran Gibbs, the left-back appears set for a move to the Portuguese champions in a reported £3.2m deal.
Traore's agent Richard des Voeux told the A Bola newspaper: "A number of European clubs were interested in Armand, but the Benfica option is more important in many aspects.
"The interest is real and we are at a sensitive stage (of negotiations).
"Armand is aware of contacts between Benfica and Arsenal.
"Benfica are a wonderful club that would interest any player.
"Obviously, Armand is very interested and excited about the possibility of coming to play at Benfica.
"Nothing is finalised, but things can be decided very soon."