Di Natale, 34, has not played for his country since Cesare Prandelli replaced Marcello Lippi following Italy's first-round exit in South Africa, despite finishing as Serie A top-scorer with unfashionable Udinese in the previous two seasons. He is also among the leading scorers this season with 23 goals. The last of those strikes helped secure Champions League football for the unfashionable northern club for a second straight season.
There were no surprise omissions with Mario Balotelli making the list despite warnings about his disciplinary and off-the-field problems.
Verratti is one of two Serie B players along with defender Angelo Ogbonna of Torino.
The Italian federation (FIGC) said the final 23-man squad would be announced on May 29.
Defenders: Ignazio Abate (AC Milan), Davide Astori (Cagliari), Federico Balzaretti (Palermo), Andrea Barzagli (Juventus), Salvatore Bocchetti (Rubin Kazan), Leonardo Bonucci (Juventus), Giorigo Chiellini (Juventus), Domenico Criscito (Zenit San Petersburg), Christian Maggio (Napoli), Angelo Ogbonna (Torino), Andrea Ranocchia (Inter)
Midfielders: Luca Cigarini (Atalanta), Daniele De Rossi (Roma), Alessandro Diamanti (Bologna), Emanuele Giaccherini (Juventus), Claudio Marchisio (Juventus), Riccardo Montolivo (Fiorentina), Thiago Motta (Paris St Germain), Antonio Nocerino (Milan), Andrea Pirlo (Juventus), Ezequiel Schelotto (Atalanta), Marco Verratti (Pescara)