The Grifone are one point adrift of safety and embroiled in what appears to be a three-team battle to avoid two relegation berths to Serie B while they travel to Chievo.
"We have got to have the hunger to tear to pieces anybody who wants to prevent us from reaching our objective," Ballardini said.
"We are aware of the situation, which is why we need to be particularly careful against a side like Chievo, who are compact and capable of hitting you on the break."
A draw with Atalanta last weekend left Genoa in serious relegation danger, but Ballardini has shrugged off the pressure.
"I'm not scared of the league table," he said. "What matters is that everybody works for the common good.
"We will get the results we need just as long as we all think of our common interests.
"There can be no excuses because you have got to overcome difficulties and if we don't understand this, then we would be in trouble."
Chievo showed a week ago that they are not going to do any favours to the sides below them.
A 1-0 win in Siena lifted them 10 points clear of the relegation zone and they now want to guarantee their place in the top flight with a win at the Stadio Bentegodi.
"Beating Genoa would seal our safety," said coach Eugenio Corini. "We've now got to complete the job.
"We have the chance to seal mathematical safety at the Bentegodi."