Gattuso, who replaced the sacked Luciano Spalletti in June, has also selected 20-year-old Inter Milan striker Francesco Pio Esposito and Bologna midfielder Giovanni Fabbian, both included in the senior squad for the first time.
Italy, who failed to qualify for the previous two World Cups, are third in Group I on three points, following a 3-0 loss in Norway and a 2-0 win over Moldova.
Norway, whose win over Italy led to Spalletti's dismissal, are top on 12 points after four games, while Israel are second with six points from three matches.
Leoni joined Liverpool earlier this month for a reported 26 million pounds, after making 17 Serie A appearances with Parma last season, and has yet to make his debut for the Premier League side.
Pio Esposito recently returned to Inter after a loan spell at Spezia in Serie B, and made his senior debut for the club at the Club World Cup, replacing his brother Sebastiano against Urawa Red Diamonds. He then scored on his first start, against River Plate.
Gattuso has also selected Gianluigi Donnarumma, despite the keeper's current problems at Paris Saint-Germain, where he has been told to find a new club and is no longer a part of manager Luis Enrique's plans.
Italy host Estonia in Bergamo on September 5th and travel to Debrecen in Hungary for their away game with Israel three days later.
Italy squad
Goalkeepers: Gianluigi Donnarumma (Paris Saint-Germain), Marco Carnesecchi (Atalanta), Alex Meret (Napoli), Guglielmo Vicario (Tottenham Hotspur)
Defenders: Alessandro Bastoni (Inter Milan), Raoul Bellanova (Atalanta), Riccardo Calafiori (Arsenal), Andrea Cambiaso (Juventus), Giovanni Di Lorenzo (Napoli), Federico Dimarco (Inter Milan), Federico Gatti (Juventus), Giovanni Leoni (Liverpool), Gianluca Mancini (Roma)
Midfielders: Nicolo Barella (Inter Milan), Giovanni Fabbian (Bologna), Davide Frattesi (Inter Milan), Manuel Locatelli (Juventus), Nicolo Rovella (Lazio), Sandro Tonali (Newcastle United)
Forwards: Francesco Pio Esposito (Inter Milan), Moise Kean (Fiorentina), Daniel Maldini (Atalanta), Riccardo Orsolini (Bologna), Matteo Politano (Napoli), Giacomo Raspadori (Atletico Madrid), Mateo Retegui (Al Qadsiah), Gianluca Scamacca (Atalanta), Mattia Zaccagni (Lazio)
