"I think that Libya will be liberated quickly and that the situation will be resolved in short notice," Frattini said on La7 television.
"In the UN resolution no violent collapse of the regime" is foreseen, but there is "an implicit pre-condition, unwritten, that I read as: Qadhafi must go," he said.
"I think the African Union has the possibility of coming up with a useful proposition that will push Qadhafi to give up power," he said.
Frattini did not provide details, but on Sunday he set out the broad outlines of a diplomatic plan to resolve the crisis in Libya that could include exile for Qadhafi.
More than 35 countries will attend a conference in London on Tuesday to map out a post-Qadhafi future for Libya.
Libya was an Italian colony between 1911 and 1942 and is Italy's top trade partner.