Chievo have won just one of their past 11 fixtures and lie 17th in the standings, level on 21 points with Livorno, who are in the relegation zone.
Genoa are riding a four-match unbeaten run but Gasperini insists they cannot take victory for granted.
"Chievo are going through a delicate period," Gasperini said. "But they will be eager to turn the page on Sunday in front of their fans and we must be prepare for a difficult game in Verona."
Last weekend's 2-0 triumph over Catania extended Genoa's unbeaten run to four games and lifted the Grifoni to 11th place.
"We are going through a good spell and we hope it lasts as long as possible," Gasperini said. "We are growing and this is an important sign.
"We are on the right path because of our current position in the standings that allows us to play without any worries in our heads."
Chievo lost 2-1 at Atalanta last weekend to suffer their fourth defeat in their last five games.
The Flying Donkeys have won just one of their last five games at home and know that anything but a win on Sunday could see them drop into the relegation zone.
"We cannot give up," Chievo coach Eugenio Corini said. "Despite the loss, we produced a good performance against Atalanta.
"This performance should give us a boost in confidence ahead of our game against Genoa."
Corini will have to do without defenders Bostjan Cesar, Genaro Sardo and Dario Dainelli, all suspended this weekend.
The visitors will be without defender Nicolas Burdisso and midfielder Andrea Bertolacci, both serving a one-match ban.