Mandorlini, who won the trophy as an Inter Milan player in 1989, saw Saturday's Serie B game at Cittadella abandoned due to poor visibility with the hosts leading 2-1.
With a money-spinning trip to Inter at stake, he told hellasverona.it: "We must go to Palermo and give it 100%.
"It's been many years since there was such fog (in Cittadella) so maybe it is some sort of omen. It's our turn, we have a chance to shine and we will enjoy it. I believe in these lads."
Like Verona, Palermo have reached three finals but are yet to win the competition.
Rosanero boss Gian Piero Gasperini told La Repubblica: "Massimo Donati will play because he's suspended in the league. Francesco Benussi will play too."
Verona's fellow promotion hopefuls Juve Stabia face a tricky tie to high-flying Fiorentina - who have won the cup six times - after reaching the fourth round with a shock victory over Sampdoria.
Veteran Viola striker Luca Toni is unlikely to feature against the south-coast outfit after colliding with Torino's Kamil Glik on Sunday.
Three-time finalists Atalanta suffered a surprise exit to lowly Gubbio in last season's third round but a trip to Roma is up for grabs should the Bergamo club get past Serie B strugglers Cesena.
Reggina sit one place behind Cesena in 18th and are the lowest placed team left in the competition, with only recent quarter-finalists Chievo standing in the way of a meeting with AC Milan.
Livorno may have lost out to Chievo in the third round last year but Bologna are vulnerable and floundering in the Serie A relegation zone. Cup holders Napoli will face the winners of the Stadio Renato Dall'Ara clash.
Elsewhere, five-time winners Torino bid to reach their 14th final by overcoming Siena at the Stadio Artemio Franchi, with Lazio waiting in the next round.