Talks to form a coalition broke down on Saturday
Kenya's president and prime minister-designate failed to reach an agreement on Sunday to end the impasse over a power-sharing cabinet.
But President Mwai Kibaki and Raila Odinga insisted they had made "substantial progress", and that they expected to clinch a deal on Monday.
However, sources tell the BBC there is little chance of a breakthrough, with wrangling over key ministries.
A power-sharing deal was reached in February to end months of violence.
Nationwide clashes followed disputed presidential elections last December.
The power-sharing deal created the post of prime minister, which is to be filled by Mr Odinga.
Agreement was meant to be reached on the other posts on Saturday, with the coalition cabinet named on Sunday.
But instead, Saturday saw Mr Odinga's Orange Democratic Movement (ODM) walk out of talks about who would fill the other cabinet posts.
An ODM spokesman accused Mr Kibaki's Party of National Unity (PNU) of reneging on an earlier deal by keeping all the major ministries.
The PNU denied this, and said the opposition had failed to submit a list of nominees.
The BBC's Adam Mynott, in Nairobi, says the principal difficulty facing President Kibaki is that he has already appointed half of his cabinet.
If he is to approve a grand coalition government, he must effectively sack a number of loyal allies from cabinet positions he awarded them just two-and-a-half months ago after his election victory.
A joint statement was issued by Mr Kibaki and Mr Odinga on Sunday as the talks broke up for the day.
"We have had a lengthy consultation throughout the day on the formation of a grand coalition government. In this regard we have made substantial progress," the statement, quoted by Reuters news agency, said.
"We appeal to all Kenyans to be patient and assure them that we expect to successfully conclude the consultations tomorrow."
However, some sources have told the BBC there is deadlock over five key ministries - Foreign Affairs, Local Government, Energy, Cabinet Affairs and Transport - and there is little chance of a deal being reached on Monday.
Some 1,500 people died and 600,000 were displaced during the violence that followed December's disputed elections.
Many thousands have yet to return to their homes.