The 24-year-old has made no secret the Gunners would be his preferred destination were the French club ready to sell.
However, while Arsene Wenger is said to be keen to bolster his squad, suggestions a £10million deal is about to be completed would appear somewhat premature.
Lille president Seydoux told Radio Monte Carlo: "We know that Gervinho is keen on Arsenal. For the moment, there has been simple contact, but we have not received a concrete offer yet."
Arsenal have also been linked with Lille's Belgian starlet Eden Hazard, but Seydoux maintained the 20-year-old would remain at their club.
It has so far been something of a slow transfer window for the Gunners, with young defender Carl Jenkinson so far the only confirmed addition in a £1m deal from Charlton.
However, that does not mean the Gunners have been idle in their search for new talent to help end a six-season trophy drought following an implosion over the closing months of the last campaign.
The addition of Southampton starlet Alex Oxlade-Chamberlain is expected to be confirmed at the start of July ahead of Arsenal's Far East tour.
However, the quest for more experienced cover, particularly in defence continues to prove a source of frustration.
It appears Blackburn are holding out for an increased fee for centre-half Christopher Samba, with Bolton's Gary Cahill and Everton's Phil Jagielka other options, if likely to be more expensive.
Spain's Under-21 midfielder Juan Mata is another reported target, rated at around £18m by Valencia, while the Gunners are also said to be tracking Argentina youngster Ricky Alvarez.
Much could depend on whether captain Cesc Fabregas is allowed to rejoin Barcelona for a cut-price £30m, and also whether France midfielder Samir Nasri puts pen to paper on a new contract.
Full-back Gael Clichy is another whose current deal expires next summer, and so could move on if no agreement is reached, with Liverpool and Roma possible destinations.
Wenger will also look to jettison some of his fringe players, with the likes of Denilson and Nicklas Bendtner expected to move on ahead of the new campaign.