Kibaki repeated the power-sharing offer to Jendayi Frazer, the US assistant secretary for African affairs, according to Isaiya Kabira, the director of the presidential news service.
Kabira offered no details and would not say whether it was a formal offer to Odinga.
Odinga said that talks must be brokered by a mediator outside Kenya, a condition the government has flatly rejected, and insisted that the current crisis was domestic.
"Our condition is only that there is an international mediator," Odinga said after he held talks with Frazer.
John Kufuor, the president of Ghana and head of the African Union (AU) is set to visit Kenya next week.
According to Al Jazeera's Yvonne Ndege, reporting from Nairobi, Kufor's visit has come late, because he was supposed to be one of the first international mediators to arrive in Kenya when violence erupted.
She said: "For some reason, his visit was shelved for some time."
"My sense is that Kufour's visit symbolises 'an African solution to an African problem' initiative. What will come of it is very hard to tell at this stage."
On Friday, Odinga's ODM party called for presidential re-run within 90 days, but the government shrugged off the demand, insisting that Odinga and his team should seek legal redress.
However, Odinga has said the courts are too loyal to Kibaki for this to take place.
The violence in Kenya broke out immediately after the electoral commission declared Kibaki the president on December 27, despite widespread allegations of vote-rigging.
What started as political clashes rapidly evolved into deadly tribal violence, claiming at least 360 lives and displacing at least 250,000 people, mainly in the country's Rift Valley region, home to a number of tribes supporting rival sides.
While the country now grapples with an unprecedented humanitarian crisis, Ali Mohamed Hussein, Kenya's chief of police, said that violence was in fact subsiding in the country.
"The situation in the country is reverting back to normal," he said.
However, Al Jazeera received reports of clashes in Mombasa and the Mathare slum, with rival political groups attacking each other with machetes.
Riot police opened fire to disperse the crowd in Mathare with reports stating that one man was shot and killed.
The UN warned that a full return to normalcy would take time.
Sara Cameron, Unicef Kenya's chief communication officer, said: "Even if the political situation is solved tomorrow, the force of the violence that was unleased in recent days ... has planted the seeds of a situation that could last much longer."
Amos Wako, Kenyan attorney general, has demanded an independent audit into the elections, while the post-election crisis has forced the government to delay by a week the re-opening of public schools as many students have been displaced or people are camped in school buildings.
The humanitarian crisis has also caused chaos beyond Kenya's borders, with fuel shortages disrupting transport and trade in Uganda, southern Sudan, Rwanda and the eastern Democratic Republic of Congo.