The checks were carried out at an apartment near Bari at the request of French authorities.
The Tunisian man, who was among seven arrested on Monday in connection with the attack, lived near Bari for several years before returning to France, La Stampa reported on Tuesday. The apartment was found empty, invesigators said.
The suspect allegedly supplied arms to 31-year-old Tunisian-born Mohamed Lahouaiej Bouhlel, who drove a refrigerated truck into crowds enjoying a Bastille Day fireworks display on the city's waterfront, the Promenade des Anglais, killing 84 and injuring 202.
Security was upped at the border with France on Friday as reports came in that an accomplice may have fled to Italy.
French investigators have yet to find links between Lahouaiej-Bouhlel, who had French citizenship, and the Islamic State group which claimed responsibility for the carnage, France's Interior Minister Bernard Cazeneuve said on Monday.
Lahouaiej-Bouhlel was shot dead after the attack.
On Tuesday, Italy's Foreign Ministry confirmed that five Italians were killed in the attack.