TMW says West Ham have expressed interest in Piccoli, who struck ten goals last season.
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Piccoli was sold by Atalanta to Cagliari in June for €12.5m after a season-long loan.
And the Sardinians are prepared to sell this summer for €24m, knowing both West Ham and Fiorentina are interested.
Cagliari will initially demand €30m to sell, but are prepared to cash in for less and have set their limit at €24m.