The country has been in political deadlock following inconclusive legislative elections in March.
The biggest winner in the poll was the pro-Russian Party of Regions, but together three former Orange Revolution allies could hold more seats in parliament.
President Viktor Yushchenko's Our Ukraine party, the party of former Prime Minister Yuliya Tymoshenko, and the Socialist Party, however, have so far failed to agree on a coalition.
Tymoshenko today again blamed Our Ukraine for the deadlock.
"I can state that as events are unfolding, I do not reject the possibility that Our Ukraine will simultaneously sign two coalition agreements: one with the Party of Regions and one with our bloc," Tymoshenko said.
No lawmaker today would predict the outcome of ongoing negotiations, but both Our Ukraine and the Socialists said they expected a deal to be struck within 24 hours.
Under the constitution, Yushchenko could dissolve parliament and call early elections if no agreement is reached by June 25.
BEHIND THE IMAGES: Click on the links below to read RFE/RL's profiles of some of the key players in Ukraine's March 26 legislative elections:
Click on the image for background and archived articles about Ukraine's March 26 elections.
Click on the image to see RFE/RL's coverage of the Ukrainian elections in Ukrainian.
Click on the image to view a photo gallery of some of the key players in the Ukrainian elections.