The former England captain joined French club on a deal to the end of the season in January, having trained with the Gunners earlier that month.
However, the Frenchman insists that the matter of the 37-year-old joining the Gunners was never discussed.
"I don't know if I would have signed him for Arsenal because it was never discussed," Wenger wrote in his Eurosport column.
"We already have enough midfielders at the club anyway and David has always said that he does not want to play for another Premier League after Manchester United.
"He trained with us at Arsenal, but it was just a cordial agreement – it wasn't even the first time he had come to train with us."
Wenger made just one signing during the January transfer window, when he bought Nacho Monreal from Malaga.