The former England centre-back made a shock return to the Gunners in January on a short-term deal, which expired at the end of the season.
The 35-year-old is now a free agent and is considering his options having held talks with Celtic while Newcastle boss Chris Hughton has denied weighing up a move for Campbell.
And although the former Tottenham and Portsmouth man has stated he would prefer to agree a new deal at the Emirates Stadium, the matter is yet to be cleared up.
"No, there is no update," Wenger told the club's official website.
Wenger has lost the services of former captain William Gallas, whose contract expired this summer, although he is thought to be closing in on a deal for 24-year-old centre-back Laurent Koscielny, who has impressed with French side Lorient.
Campbell, who began last season with an ill-fated spell in League Two with Notts County, feels he still has much to offer having made a strong finish to the campaign with Arsenal.
He was even disappointed to be overlooked for England's World Cup squad, with Fabio Capello opting to bring Ledley King and Jamie Carragher out of the international wilderness ahead of himself.