They have finished negotiations but not enough progress has been made for a deal.
A Ukraine-EU summit in Kiev has focused on a possible political and trade agreement.
But the jailing of opposition leader Yulia Tymoshenko has become a spoke in the wheel.
“Do we have the rule of law in Ukraine?” our correspondent asked the European Commission President.
“It’s a state that’s making progress on this,” said José Manuel Barroso. “And we are working to consolidate the reforms. That’s why we’re here today, to offer encouragement, so Ukraine can consolidate the rule of law.”
The European Council President says the signing of any deal depends on what he calls “political circumstances”.
Experts say Ukraine has a difficult balancing act to perform.
Volodymyr Fesenko at the Centre for Applied Political Studies told euronews: “The interest of Ukraine is in finding a certain balance in the relationships with the European Union and Russia. However, the priority is given to the European integration. As for the gas issue, it rather pushes Ukraine towards Europe. Ukraine hopes that Europe will be its ally in gas relations with Russia.”
Supporters of Yulia Tymoshenko protested near the summit, as EU officials voiced concern about what they called “politically-motivated justice”.
Our correspondent in Kiev, Sergio Cantone, says energy-related interests are dictating Ukraine’s political and legal agenda, which puts Kiev on a collision course with Brussels.