Anna German, the vice chairwoman of Yanukovych's Party of Regions, said the court deliberations were a "mere formality".
"These proceedings can't overturn the obvious: The majority of Ukrainians have voted for Yanukovych," she said.
"The entire world has recognised Yanukovych's victory."
Viktor Nebozhenko, the head of the Ukrainian Barometer polling agency, said Tymoshenko has "little chance of winning" the court appeal.
"Tymoshenko's key goal is now to stay in the prime minister's seat. She has nothing to lose and is ready to offer promises and jobs."
Tymoshenko has urged a full recount of the vote, and delivered what she said was evidence to the court on Tuesday.
But she has asked her supporters not to hold street demonstrations as they did in what became known as the 2004 Orange Revolution.
Those protests lead to a court's overturning Yanukovych's presidential election victory that year and ordering a rerun, which was won by Tymoshenko ally Viktor Yushchenko.
International observers have deemed Ukraine's latest election free and fair, and many world leaders, including Barack Obama, the US president, have already congratulated Yanukovych.