After signing Savio from Brescia for a club record £10million, technical director Gianluca Nani has identified Floccari as the man to solve the Hammers' striking woes.
With concerns about the fragile Dean Ashton's long-future and David Di Michele and Diego Tristan on season-loan longs at Upton Park, boss Gianfranco Zola needs to strengthen his strikeforce.
With 12 goals in 27 Serie A games, Floccari has attracted interest from across Europe, and Atalanta are said to be holding out for £14m.
Target: Floccari (left)
The Italian club appear resigned to losing their prize asset with Atalanta sporting director Carlo Osti remarking: 'Sergio has now reached his full potential as a footballer in this league.
'We have an agreement with the player and his agent that he will be sold at the end of the season if someone is interested,' report the Daily Mirror.
West Ham striker Ashton takes a huge step on long road back to fitnessSportsmail's Star of the Season: Have your say on who should be your team's player of the season - with NEW revised short lists!WEST HAM UNITED FC