Galliani has sold Michele di Gregorio to Juve and now Szczesny could make the opposite move.
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He told Sky Italia: "Frankly, I don't know, I haven't spoken to him yet. He knows about the interest on our part, I spoke to someone else and we'll see."
The Pole was not called up by Thiago Motta for this week's Juventus tour in Germany, with the aim of finding a new club as soon as possible.
The biggest obstacle appears to be the player's salary, with Juventus possibly having to contribute to his payment.