Senior Hamas figures gathered for the last stage of internal elections on Monday in Cairo, where two officials in the militant movement said a new leader may be announced later in the day.
Qatar-based Khaled Mashaal, who has run the Palestinian movement since 1996, is seen as the front-runner. Mashaal, 56, is backed by regional powers Qatar, Turkey and Egypt.
His re-election could revive stalled reconciliation efforts between Hamas and political rival Mahmoud Abbas, the Western-backed Palestinian president.
Hamas seized the Gaza Strip from Abbas by force in 2007, leaving Abbas with a self-rule government, the Palestinian Authority, in parts of the West Bank. Both sides have become entrenched in their territories, hampering reconciliation.
Mashaal has pushed for reconciliation, but has been blocked by Hamas hardliners in Gaza who fear a unity deal will give Abbas a new foothold in Gaza and weaken Hamas' grip on the territory.
Last year, Mashaal and Abbas, who have cordial relations, reached a deal whereby Abbas would head an interim government of technocrats in the West Bank and Gaza. This government would have paved the way for general elections.
However, the deal never got off the ground because of opposition from Hamas leaders in Gaza and senior figures in Abbas' Fatah movement.
Last week, the emir of Qatar proposed holding a reconciliation conference in Egypt in the coming weeks to set up a timetable for forming the interim government and holding elections.
Asked about the conference Monday, Abbas seemed ambivalent. Speaking in the West Bank city of Ramallah, he said he would attend such a conference if invited, but that "in principle, there are no problems between us that require all these efforts."
Hamas' internal elections, meanwhile, have dragged on for a year, in part because of logistics problems, including the difficulties of voting in the Israeli-controlled West Bank. Israel, the United States and Europe consider Hamas a terrorist organization.
The secretive movement was founded in Gaza in 1987 as an offshoot of the region's Egyptian-founded Muslim Brotherhood. Hamas leaders, including Mashaal, refuse to recognize Israel or denounce violence, Western conditions for ending a boycott of Hamas.
Still, Mashaal appears to have adopted a more pragmatic stance in recent years, expressing support for a Palestinian state in the West Bank, Gaza and east Jerusalem, lands Israel occupied in 1967. He has also agreed that a Palestinian interim government could follow the political program of Abbas who has negotiated the terms of a Palestinian state with Israeli leaders in the past.
Two Hamas officials said the vote for a new leader was likely to be held Monday evening. Mashaal's deputy, Moussa Abu Marzouk, is also among those considered for the post.
They spoke on condition of anonymity because they were not allowed to talk about the movement's secret election.
Hamas has four components - activists in Gaza, in the West Bank, in exile and those imprisoned by Israel. Each of the four groups chooses local leaders as well as delegates to an overall Shura Council. This council selects a decision-making political bureau and the head of that body - the stage now under way in Cairo.