Walter Mazzarri's side are near to completing the signings of the two Italians and one Switzerland international as they look to challenge for silverware next season
The Viola duo will be in Naples on Monday for medicals, while the Samp man is currently negotiating with the Partenopei after talks with Inter broke down.
According to Corriere dello Sport, Poli is keen on the idea of reuniting with former boss Walter Mazzarri, and would prefer to move to the Azzurri after talks with Andrea Stramaccioni's side hit a snag.
The transfers of Behrami and Gamberini, however, look slightly more straightforward, after La Viola released a statement on their official website.
"After conversations between Fiorentina and Napoli, Valon Behrami and Alessandro Gamberini are permitted to perform medical examinations with the staff of the Neapolitan team."
The Switzerland international has played 40 games for the Tuscans in 18 months with the club, while the 30-year-old Italian has made nearly 200 appearances for the Stadio Artemio Franchi side.