Tens of thousands of demonstrators are expected to swarm around the court building after opposition lawmaker Yulia Timoshenko called them to turn out to "not put pressure on it, but support honest judges".
Kiev has been awash with orange opposition banners since the 21 November election, which the opposition claims was stolen from their pro-Western leader Viktor Yushchenko by massive ballot fraud.
Their claim has been backed by parliament which decided, in a non-binding resolution, that the vote was invalid due to widespread irregularities.
As the position of Yanukovich, the declared winner, has weakened in the face of Yushchenko's "orange revolution", the pro-Russia regions in the east and the south that support Yanukovich have begun to step up their demands for autonomy.
Yanukovich met on Sunday with about 3500 local officials from 17 of Ukraine's 27 regions - which make up two-thirds of the country's population of 48 million - and warned that the country was heading towards an imminent collapse.
"Either we are capable of preserving the stability and peace in our state, or everything will collapse and very rapidly," he told the leaders of the Russian-speaking regions.
Leaders of Russian-speaking
regions are to hold a referendum
The regional leaders then said they would hold a vote on "self-defence" - a euphemism for autonomy - should Yushchenko come to power, and reserved the right to call for a 12 December referendum on their regions' territorial status in case Yanukovich was ruled to have lost the vote, the Interfax news agency reported.
The strategic coal-mining region of Donetsk became the first region to set an autonomy vote by scheduling a 5 December referendum on whether to proclaim itself a "republic".
Meanwhile in Kiev, Yushchenko told his followers that the Russian-speaking regions allied with Moscow had to be punished for threatening to break off.
"We demand the opening of a criminal inquiry against the separatist governors," Yushchenko, wearing an opposition orange scarf to protect himself from the freezing cold, told the orange flag-waving masses below him.
Yushchenko says Moscow-allied
regions should be punished
Later opposition lawmaker Yulia Timoshenko called on outgoing President Leonid Kuchma to sack Yanukovich and governors of separatist regions.
"We give him 24 hours to do that," she said.
Earlier on Sunday Kuchma said in televised remarks that a compromise over the crisis was needed to avoid "unforeseeable consequences", but a deal still seemed a long way off.
Opposition representatives warned that if talks with Yanukovich's camp failed to make progress they would call on Monday for an international mediator to intervene.
The supreme court, which has previously shown its independence from the government, could annul the elections, order a partial or full recount, or reject the appeal.
The court hearings were scheduled to begin at 11am (0900 GMT), but there was no guarantee that it would rule on the issue on Monday.
The Ukrainian parliament has
declared the vote invalid
The Ukrainian parliament had on Saturday judged the vote's second round as invalid, saying it was marred by fraud and the announced result did not reflect popular will - a statement that has no legal force, but may swing the court's decision, opposition lawmakers hoped.
The vote has not only exacerbated historical tensions between Ukraine's nationalist, Ukrainian-speaking west and the industrialised, Russian-speaking east, but reopened a cold war rift between Russia and the West.
Russia has strongly backed Yanukovich, and has been one of the few countries to recognise his victory.
Western countries have refused to accept the election results due to widespread fraud.
But Moscow has angrily accused the West of fomenting unrest to wrest Ukraine from Russia into its sphere of influence, but Western capitals say they are simply standing up for democracy.