The winger is being linked with Tottenham and Inter Milan.
Zangrillo told Radio Sportivo: "He is a young guy who's serious, and wants to have ambitions that we aren't able to guarantee at the moment.
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There's no denying that.
He has suitors both in Italy and abroad.
And it's only right for both parties to make evaluations.
Let's let the player dream. We leave the possibility open of a departure for the right offer.
We've learned to love our players.
We can have a good transfer window, and then thin that in a few years Albert can say: 'If it weren't for Genoa, I wouldn't be here'."