Dall'Oglio, who disappeared in the northern Syrian city of Raqqa on 28 July last year, is being held in Sed Tishreen jail located in the surrounding province, the daily cited activists as saying on Tuesday.
There are currently "highly delicate" negotiations talking place between Syrian rebels and jihadists from ISIS for control of the prison, where Dall'Oglio and other prisoners including French journalists are being held, according to the activists.
The Western-backed Free Syrian Army (FSA) and the jihadist Al-Nusra Front have removed barriers erected around Sed Tishreen by their former ISIS allies between Raqqa province and the Turkish border, the activists claimed.
"The nex step should be to take control of Sed Tishreen, which is in ISIS hands, avoiding an assult in order to ensure the safety of its high-profile prisoners, the activists were quoted as telling Al-Hayat.
On Monday, the UK-based Syrian Human Right Observatory monitoring group reported that FSA fighters had ousted ISIS from Raqqa, freeing more than 50 hostages in a fourth day of clashes across the north of the country.
Raqqa become an ISIS stronghold after rebels overran the city in March last year. It was the first provincial capital to fall under rebel control.
Scores of captives, among them journalists and aid workers, had reportedly been detained by ISIS in government buildings. Those freed on Monday appeared to all be Syrians. It is understood that the western captives had earlier been moved to another location.
Conflicting reports have deepened the mystery surrounding Dall'Oglio's fate. In October, an opposition activist told Adnkronos International (AKI) the priest was alive and was being well treated by his ISIS captors.
Earlier, the Vatican and the Italian government said in August they could not confirm a report by a pro-Syrian-government website that the priest had been executed by his captors.