The Frenchman wants to add the Germany international and another proven goalscorer to lighten the load on captain Robin van Persie, who has scored just under half of the Gunners' league goals this season.
The 62-year-old boss was quoted by The Daily Mail as saying: "Yes [we want Podolski], because we want to add some offensive strikers, because many times people say we rely too much on Van Persie, which is true, but if we can find world-class players, we will [challenge for the title]."
Arsenal are currently 4/9 with Paddy Power to finish above Tottenham in this year's Premier League table.
Wenger also believes that keeping a fit squad will be important after suffering throughout the season with injuries to most of his big name players.
"I just felt we had two weak periods in the season and you can only afford one," he continued.
"I knew when we were 17th [in August] that we cannot afford any weak periods anymore, so when that happened in January it was very difficult.
"If you look at the circumstances of the [second] blip, it was down to the fact we had no full-backs. Overall since October, since the team has gelled, we are not on too bad a run.
"Manchester City have had the opposite; they started in the way we are now. It is difficult for everyone to maintain that."
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