Gigliati coach Vincenzo Montella has struggled to field a full strength attack this season because of injuries to Giuseppe Rossi and Federico Bernardeschi so the Viola are looking for more options in attack.
According to Firenzeviola.it, Fiorentina want to acquire Di Santo in January and a deal is possible on the basis that he holds both an Argentinian and Italian passport.
Although Werder Bremen are sitting on the bottom of the Bundesliga table, Di Santo has scored six goals in 10 league matches this season.
Before he joined the Gruen-Weissen last season, Di Santo was best known for his time with English clubs Chelsea and Wigan Athletic, in which he spent three season with the Latics.
Di Santo has won three caps for Argentina and he made the Albiceleste’s provisional squad for the 2014 FIFA World Cup only to be cut from the final 23.
Follow Vito Doria on Twitter: @VitoCDoria