Several media sources have claimed over the past couple of days that the Cologne striker, whose contract expires in 2013, will move to London in a £10.9 million deal this summer.
And Gunners defender Per Mertesacker claims that Podolski, his international team-mate, has contacted him regarding the possibility of a transfer to Arsenal. But Wenger said: "I don't have a lot to say about Podolski. If we sign a player we will inform you."
Podolski has expressed frustration with life at Cologne, who are currently 14th in the Bundesliga - and the club are thought to be willing to get his wages, believed to be in excess of £100,000-a-week, off the bill.
The 26-year-old, who had three years at Bayern Munich before returning to his hometown club in 2009, has scored 43 times in 95 games for Germany.
Wenger says that should Podolski arrive, it would have no bearing on the future of skipper Robin van Persie - another whose contract runs out in summer 2013.