Reports had suggested that the Germany international had agreed a £10.9m move to the North London club, something that Cologne refused to comment on.
However, Wenger has said that no deal has been reached for the player just yet.
"If we sign a player we will inform you and at the moment we have not signed anybody," said the Frenchman.
"There's still no agreement. Podolski is a good player. I wouldn't deny that."
Arsenal currently sit fourth in the Premier League, four points behind third-placed Tottenham Hotspur.