Podolski scored twice in his first pre-season friendly of the summer against former club FC Cologne as Arsenal ran out 4-0 winners.
Wenger told reporters: "He is not yet 100% fit, he is not running at 100%, but we are working on that.
"Of course you know from his time in Cologne he can score and he showed that again today.
"He will be in the squad for the first match but I can't tell you yet whether he will start."
Arsenal begin their Premier League campaign at home to Sunderland on Saturday, August 18.