Sampdoria forward Quagliarella is the top scorer in Serie A, having already netted 20 goals in the most prolific season of his career and will hope to make his debut in Italy colours in the coming games.
Roberto Mancini handed the 36-year-old a recall for a training camp in February and he is now in line to face Finland and Liechtenstein as the Azzurri commence their Group J campaign.
Marseille striker Balotelli is still absent, though, despite scoring five times in his last seven Ligue 1 games, with uncapped Cagliari attacker Leonardo Pavoletti, Juventus teenager Moise Kean and Lazio centre-forward Ciro Immobile preferred.
There are six Juve players selected among the 29-man group, including five-cap full-back Leonardo Spinazzola, who impressed on his Champions League debut against Atletico Madrid on Tuesday.
Along with Pavoletti, talented Roma youngster Nicolo Zaniolo is one of five players in contention for a maiden international appearance.
Italy squad in full:
Alessio Cragno (Cagliari), Gianluigi Donnarumma (AC Milan), Mattia Perin (Juventus), Salvatore Sirigu (Torino); Cristiano Biraghi (Fiorentina), Leonardo Bonucci (Juventus), Giorgio Chiellini (Juventus), Alessandro Florenzi (Roma), Armando Izzo (Torino), Gianluca Mancini (Atalanta), Cristiano Piccini (Valencia), Alessio Romagnoli (AC Milan), Leonardo Spinazzola (Juventus); Nicolo Barella (Cagliari), Bryan Cristante (Roma), Jorginho (Chelsea), Stefano Sensi (Sassuolo), Marco Verratti (Paris Saint-Germain), Nicolo Zaniolo (Roma); Federico Bernardeschi (Juventus), Federico Chiesa (Fiorentina), Stephan El Shaarawy (Roma), Vincenzo Grifo (Freiburg), Ciro Immobile (Lazio), Moise Kean (Juventus), Kevin Lasagna (Udinese), Leonardo Pavoletti (Cagliari), Matteo Politano (Inter), Fabio Quagliarella (Sampdoria).