The England international looks certain to leave the Trotters in January, but Wenger has insisted that Arsenal are not in the race.
"We have plenty in the middle, we have plenty of centre-backs ... we are not looking for any centre-back," Wenger told Sky Sports News.
When quizzed upon a bid for Gary Cahill, Wenger added: "Centre-back, no chance".
"I haven't made any enquiry yet, at all, for the moment there is no Wayne Bridge on the table."
Arsenal continue their league campaign at home to Wolves on Tuesday afternoon.