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.
"Look, the first proposal was farcical. Of course [we are open to discussion]. After they come back a bit more serious then we will see what happens," he told reporters.
"Inevitable in a transfer is very difficult to say, but we’ll 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.