The five residents are suspected of being close to jihadist groups, with some thought to have recruited fighters for Iraq and Syria, the newspaper said.
The investigation is part of a terrorism probe opened by the district attorney of Venice.
Earlier this week, it was reported that around 50 Italians have been recruited by the Islamic State in Iraq and Syria (Isis), the majority from non-immigrant families.
Isis has grown in recent months to become one of the main jihadist groups fighting government forces in Syria and Iraq.
According to the International Centre for the Study of Radicalisation (ICSR), based at King’s College London, there are up to 11,000 foreign fighters in Syria alone.
Between 396 and 1,937 are thought to come from western Europe, with the highest concentration from Belgium.
Up to 296 Belgians are fighting in Syria, 27 per capita, compared to a high estimate of 50 from Italy and 1 per capita. In western Europe, France has the highest number of foreign fighters in Syria – 412 – followed by the UK with up to 366.