Hamas recently completed the formation of a new Shura Council of more than 80 members, a consultative body largely composed of religious scholars, as well as a new 18-member political bureau, the official said.
Since the war in Gaza began after Hamas's October 7, 2023 attack on Israel, Israeli forces have killed several Hamas leaders, including two former chiefs.
"The movement has completed its internal elections in the three regions and has reached the final stage of selecting the head of the political bureau," the official said, speaking on condition of anonymity as he was not authorised to speak publicly.
He said the race for the group's leadership was now between Khaled Meshaal and Khalil al-Hayya.
A second Hamas source confirmed the development, while a third source said the new leader would lead the movement only "for one year".
Despite a US-brokered ceasefire that entered its second phase last month, violence has continued in Gaza, with Israel and Hamas blaming each other for violating the agreement.
Members of the council are elected every four years by representatives from Hamas's three branches: the Gaza Strip, the occupied West Bank and the movement's external leadership.
Hamas prisoners in Israeli jails are also eligible to vote.
The council subsequently elects the political bureau, which in turn selects the head of the movement.