Odinga lost in a narrow March 4 race to challenger Deputy Prime Minister Uhuru Kenyatta, who passed the 50 percent threshold for victory by around 4,100 votes.
The Supreme Court in Kenya called for a recount from 22 polling stations. Odinga said the vote count was rigged in favor of Kenyatta and called on supporters to remain upbeat ahead of a high court announcement Sunday.
"Things will soon be all right," he was quoted by The Daily Nation newspaper in Kenya as saying. "Please let's no one lose hope."
Odinga's challenge to the 2007 elections preceded political violence in Kenya that left more than 1,000 people dead.
Kenyatta faces the International Criminal Court in July on charges of committing crimes against humanity during the post-election violence. He's said he expects the court to drop the case against him.
There were few reports of violence surrounding the March 4 election. International observers described this year's election as generally fair.