Yanukovich beat arch-rival Tymoshenko in a presidential election last month, raising hopes that a new political order could put to rest years of turmoil. Yanukovich was in Brussels on Monday on his first visit as head of state.
Analysts said the fact that leaders in parliament agreed to hold the vote showed Yanukovich's Regions Party was confident it had enough support - including dozens of members from Tymoshenko's coalition - to pass the motion in parliament.
But factions in the parliament are famously fickle and several key players sounded ambiguous notes.
If the vote succeeds, Tymoshenko and her government will remain until a new cabinet replaces them. In the meantime, parliament faces weeks of horsetrading to replace the ruling coalition and create a new government.
The fiery prime minister was in a typically combative mood, telling a cabinet meeting the vote should be held as soon as possible, so that all was "made clear" in parliament.
She said the vote would show who "supports anti-Ukrainian, anti-democratic, anti-European development of the state with all its corruption of oligarchs, and who is for the development of democracy, the development of Ukraine's European path....”
The victory of Yanukovich - a Moscow-backed candidate who was denied the presidency by the 2004 "Orange Revolution" protests against vote-rigging in his favor - is expected to tilt Ukraine back toward its former Soviet master.
He travels to Moscow on Friday.
But in a sign that he wants to strike a balance between improved relations with Moscow and close ties to the European Union, Yanukovich chose Brussels for his first visit, where he promised he would keep Ukraine on a path of reform.
Any new government will have to tackle a deep financial crisis which pushed Ukraine's gross domestic product (GDP) down by 15 percent last year and restart talks with the International Monetary Fund on a suspended $16.4 billion bailout package.
The Regions Party, with 171 members in the assembly, needs to garner 226 votes in total from the 450-seat parliament to pass the no confidence vote. It can gain support quite easily from parties that do not belong to Tymoshenko's coalition.
But it also needs to steal members of the Our Ukraine Party of former President Viktor Yushchenko and members supporting Parliament Speaker Volodymyr Lytvyn. Both groups are currently part of a coalition with Tymoshenko's bloc.
Lytvyn said the chances of the motion passing were "50-50,” according to a statement on the parliament's Web site, without elaborating which way his supporters would vote. He himself cannot vote as speaker.
A deputy leader of Our Ukraine, Taras Stetskyv, said the three coalition parties held a meeting on Monday but only 25 of over 70 from his faction turned up while Lytvyn's supporters will decide which way to vote on Tuesday.
If the vote passes and the Tymoshenko-led alliance formally collapses, the various parliamentary factions have 30 days to form a new coalition and 60 days to form a new government.
If this proves impossible, President Yanukovich has the right to call a new parliamentary election - a scenario feared by investors because it would prolong uncertainty for months as Ukraine continues to struggle without IMF funds.
