Clashes between Kibaki and Odinga supporters, ethnic unrest and a brutal crackdown by the security forces have killed at least 700 people over the past month.
"We are determined to work with the parties to find a solution as quickly as possible," Annan said after landing in Nairobi late on Tuesday.
"We want to determine by tomorrow how quickly the parties want to work with us."
Odinga's Orange Democratic Movement (ODM) has called for another "peaceful protest" on Thursday, in defiance of a ban.
But Salim Lone, Odinga's spokesman, said on Wednesday that ODM would be willing to reconsider.
"If Mr Kofi Annan asks ODM to cancel the rally, we will of course consider it very seriously," he said.
Yvonne Ndege, Al Jazeera's correspondent in Nairobi, said that a representative of the opposition has told her that they are considering a request by Annan for talks.
Past efforts failed
Annan's mission follows a similar attempt by John Kufuor, the African Union head and president of Ghana.
Kufuour failed to get Kibaki and Odinga to meet.
Yoweri Museveni, the Ugandan president, also arrived on Tuesday to join in the mediation efforts.
But the opposition distrusts him because he is one of few African leaders to have congratulated Kibaki on his victory.
Odinga says a December 27 poll that returned Kibaki to power was fraudulent.
His supporters have taken to the streets and mobs mostly targeting Kibaki's Kikuyu tribe have hacked people to death and burnt homes.
There have also been reprisal killings.Memorial gathering
The opposition will hold a memorial gathering starting at a mortuary then proceeding to a big football field near the Kibera slum in Nairobi, the capital, on Wednesday for those who have died in the unrest.
Police have banned all rallies and have broken up previous gatherings of supporters from both sides but have said they will allow the memorial gathering to go ahead.
Odinga and Kibaki have so far refused to speak to each other despite pressure from Western powers like the US, Britain and the EU.
"We expect all parties to enter into dialogue in good faith and to seize this opportunity to end the suffering and uncertainty," Annan said.
At least 250,000 Kenyans have been displaced by the fighting and has cost east Africa's biggest economy more than $1bn and has choked fuel supplies and trade to landlocked neighbours like Uganda.