"Negotiations on Shalit will resume after Eid al-Adha in Cairo on Tuesday," the official told AFP on Thursday on condition of anonymity.
The Hamas delegation, which visited the Syrian capital on Wednesday to meet the movement's leadership in exile, returned to the Gaza Strip via Cairo, he added, while refusing to detail the content of the discussions.
Shalit was captured by Palestinian militants including Hamas in a cross-border raid from the Gaza Strip in 2006.
Hamas, which has controlled the territory since June 2007, is demanding that more than 450 Palestinian prisoners in Israeli jails be released in exchange for the soldier.
But Israel is refusing to release some of the detainees, blocking the chance of any agreement being reached, an official close to the talks said on Wednesday.
The same official said reports of an imminent prisoner exchange were "premature."
Both Hamas and Israel earlier this week reported progress in the negotiations, which have been mediated by Egypt and Germany, but played down reports of a quick deal.
Hamas on Wednesday blamed the delay on Israel, which "has not yet answered the demands of the Palestinian factions," senior Hamas official Khalil al-Haya said.