The 26-year-old is widely expected to leave the Bundesliga club in the summer, with coach Stale Solbakken already admitting that the club will not stand in the way of a transfer.
Arsenal have been suggested as Podolski's likeliest destination, a possibility that has been backed by Oliver Bierhoff.
However, Express reports that the Serie A duo are also in the running for Podolski, which could give the Germany international some food for thought.
Schalke are reportedly ready to offer Podolski €6 million per annum to convince him to move to Gelsenkirchen, but it is understood that the striker's strong ties with Koln will prevent him from leaving the club for another German side.
Podolski's contract is due to expire in 2013.
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