President Uhuru Kenyatta, who was declared the victor in the August vote, wants to press ahead with Thursday's election despite concerns about its credibility.
In the case, Pokot South MP David Pkosing had argued that Mr Odinga must comply with the Supreme Court decision that ordered a fresh presidential election.
The court hearing will occur even though Kenya's interior ministry has declared Wednesday and Thursday to be public holidays.
The High Court has dismissed a petition seeking to have National Super Alliance leader Raila Odinga take part in the repeat presidential election scheduled for Thursday, October 26.
Kenyan police fired teargas and shots in the air to scatter a small number of demonstrators in Nairobi on Tuesday.
Human rights activists have said police fatally shot 67 people since the August 8 election whose annulment by the Supreme Court opened the way to the new vote.
NASA leader Raila Odinga addressing his supporters in the past. He called the Supreme Court justices "crooks" after they nullified his re-election.More news: It's 2017 And Nivea Wants To 'Visibly Lighten' Dark Skin
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The Judge acknowledged that there is an active and critical ongoing presidential process in the country and if Pkosing's orders are granted, the court will be going overboard in determining the question of validity of the same process way beyond its jurisdiction.
After the 2007 election, which observers agreed was deeply flawed, politically-motivated tribal violence left 1,100 dead.
IEBC chairman Wafula Chebukati's announcement that the election may not be credible has fulled calls that the exercise should be cancelled.
Mr Khalef Khalifa, Mr Samuel Mohochi and Mr Gacheke Gachuhi claim the electoral commission is divided and can not guarantee a fair and credible poll. She then fled to the United States, saying she feared for her safety.
Khelef Khalifa, a petitioner and human rights activist, said the goal is to secure a postponement of Kenya's elections until the electoral commission is prepared to deliver a credible vote.
They said that the credibility of the vote is not assured, citing political interference among other concerns.