Both Venezia and Vicenza have pedigree in the competition, with the latter having enjoyed the more recent success.
Vicenza were victorious in 1997, while Venezia's triumph came way back in 1941, however, both teams have seen better days and now reside in the newly realigned 60-team Lega Pro, the third tier of Italian football.
But, while their glory days may be long gone, the duo have the chance to try to evoke memories of their former successes this weekend as they take on fourth-tier Taranto and newly promoted Lega Pro side Bassano Virtus respectively.
A number of formerly well-established Serie A clubs will be competing in the opening round, which features a total of 18 ties.
Lecce, who were in the top flight as recently as 2012, take on Foligno, while Reggina start their season against Casertana following relegation from Serie B last term.
Reggina's arch-rivals Messina visit Pontedra, and Pisa, Cremonese and Sudtirol should all have a good chance of progressing against RapalloBogliasco, Nuova Cosenza and Teramo.
Monza will look to get their cup campaign on track against Olginatese, Alessandria take on Salernitana and last season's bottom club in Serie B Juve Stabia face Prato.
AlbinoLeffe will be able to size up Renate in a clash between two teams in Group A of the Lega Pro, Benevento meet Correggese and L'Aquila host Alto Vicentino.
Elsewhere, FeralpiSalo, Catanzaro, Savona and Como are in action against Santarcangelo, Akragas, Terracina Calcio, Matelica Calcio.