Correspondents say it could be the last chance for Mr Mbeki's mediation
Zimbabwean President Robert Mugabe and opposition leader Morgan Tsvangirai have both spoken positively about their talks in Harare on sharing power.
After two days of discussions in a hotel, the two men both said they hoped to address the outstanding issues between them on Wednesday.
"I must say that there is a positive development," Mr Tsvangirai said.
Speaking to reporters, Mr Mugabe noted there had been "progress - and lack of it - in some areas".
A special summit meeting on Zimbabwe, due to be held in Swaziland on Wednesday, has been postponed by a day because South Africa's President Thabo Mbeki is remaining in Harare to conduct the negotiations, a South African official told the BBC.
Zimbabwe's state-owned Herald newspaper reports that Mr Mugabe, Mr Tsvangirai and Arthur Mutambara, head of a smaller opposition faction, held individual talks with Mr Mbeki on Tuesday and then the three of them met without the South African leader.
Source in Mr Tsvangirai's Movement for Democratic Change (MDC) say they are now proposing that Mr Tsvangirai be named prime minister, with full authority over all the ministers, while President Mugabe chairs a new National Security Council.
Morgan Tsvangirai has said no deal would be better than a bad one
This would mean he keep some authority over the security forces.
Several Zimbabweans security chiefs have said they would refuse to take orders from Mr Tsvangirai, who they see as being a Western stooge.
The MDC and human rights groups have accused the army of spearheading a campaign of violence against opposition activists ahead of June's presidential run-off.
Mr Mugabe has threatened to form a government alone if a deal is not reached this week.
Donors have been withholding aid to rescue the collapsing economy until the opposition are given real power in government.
Talks between the government and the MDC in August broke down after they agreed that Mr Tsvangirai would be named prime minister while Mr Mugabe remained president, but failed to agree on how to share powers.
'Finality and closure'
"Nothing has been concluded yet but we are hoping that tomorrow [Wednesday] we will be able to look at the outstanding issues," Mr Tsvangirai was quoted as saying by Reuters news agency.
Mr Mugabe said "one or two areas" were still outstanding.
"We are still going to talk. We are finishing tomorrow [Wednesday]," he said, according to Reuters.
Mr Mutambara talked of "tremendous progress".
"We hope tomorrow [Wednesday], we will be able to bring finality and closure to the dialogue process," he said.
The MDC leader gained more votes than Mr Mugabe in March elections but official results say he did not pass the 50% threshold for outright victory.
Mr Tsvangirai pulled out of the June run-off, saying some 200 of his supporters had been killed and 200,000 forced from their homes in a campaign of violence led by the army and supporters of the ruling Zanu-PF.
Zanu-PF has denied the claims and accused the MDC of both exaggerating the scale of the violence and being responsible for it.