Podolski has been a peripheral figure for the north London club this season, making just 13 appearances – and two starts – in all competitions.
The 29-year-old has scored three goals this term, but has seemingly been unable to convince Wenger of his capabilities long-term.
Wenger had previously rejected speculation Podolski could leave the club in January, while the player himself has voiced his desire to play more regularly.
Speaking after Arsenal's 2-0 defeat to Southampton, Wenger said the Serie A club had made a second offer for Podolski – who missed the game with a tight groin - after the first was laughed off.
He said: "The first proposal was farcical, after they came back a bit more serious so we will see what happens now.
"In the transfer window it is very difficult to say, we will see what happens."
Podolski's last Arsenal appearance was 17-minute substitute appearance against Newcastle United in mid-December, and he has been an unused sub in three matches since.
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