The Mirror says the Upton Park club agreed a £9million deal for Brescia playmaker Savio Nsereko during the January transfer window.
And now Italian technical director Gianluca Nani has identified Floccari, 27, as the man to lead the Hammers attack next season.
The Atalanta striker has scored 12 goals in 27 games in Serie A this season and is on the fringes of the Italian national squad.
His form has also attracted the interest of Newcastle as well as Juventus, Roma, Villarreal, Wolfsburg and Zenit St Petersburg. Atalanta, who turned down an £8m bid for him last season, are hoping to start an auction to sell their star player for £14m.