"We agreed at the (security) organ that the agreement should be signed within the period of the summit," the minister who requested anonymity said.
The trioka that met on Friday evening includes Angola, Tanzania and Swaziland.
Zimbabwe’s President Robert Mugabe and the leaders of both of the country’s opposition factions separately addressed the meeting.
Referring to the Zimbabwean officials, the minister said: "All the parties appear to be agreeable (to reaching an agreement this weekend), but it’s a wait and see situation."
A South African official close to the talks said remaining sticking points in the negotiations include whether Mugabe will retain the right to hire and fire ministers, as his party wants.
The opposition Movement for Democratic Change argues its leader Morgan Tsvangirai should have that power under a power-sharing deal, according to the official.
A timeframe for how long a government of national unity would remain in place is also being debated, the official said, with the MDC pushing for a shorter arrangement and the ruling Zanu-PF wanting a longer length of time.
The opposition also wants a clause included to specify that new elections would be held within 90 days if any of the parties were to withdraw from the government of national unity, said the official.
Zimbabwe’s political crisis intensified after Mugabe’s re-election in a June presidential run-off widely condemned as a sham.
Tsvangirai boycotted the poll despite finishing ahead of Mugabe in the March first round of the election, citing rising violence against his supporters.