Frontrunners include the secretary general of the Syrian National Coalition Mustafa al-Sabbagh, and Ahmad Assi Jarba, representing the faction of secular dissident Michel Kilo.
Recognised by dozens of states and organisations as the legitimate representative of the Syrian people, the umbrella group is seeking a successor to interim president Georges Sabra, who may also seek nomination.
The opposition has been rudderless after the departure in May of Ahmad Moaz al-Khatib in protest at the world's "inaction" over Syria's civil war.
"Informally, the names of Burhan Ghalioun, Georges Sabra and Louay Safi are also being discussed. But of course we never know."
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The nomination of a new chief had initially been mooted for the end of May but was postponed after eight days of talks stalled in the face of conflicting views on the future direction of the coalition.
Under pressure from, among others, Saudi Arabia and Qatar, the opposition agreed in the May meeting to accept new groups under the umbrella of the coalition, lessening the influence of a strong Muslim Brotherhood faction backed by Doha.
The coalition will also likely discuss a future peace conference dubbed "Geneva 2" they have deliberated over attending, named after a meeting in the Swiss city a year ago that set up the transitional government but did not agree on the fate of Syria's President Bashar al-Assad.
The assembly takes place after a series of setbacks for the rebels including the fall of Qusayr to Assad's forces, a former rebel bastion near the Lebanese border, aided by fighters from Lebanon's Shiite Hezbollah movement.