But if the chance of signature doesn't look good for Friday, the EU does have the tentative schedule for a bilateral summit with Ukraine in late winter or early spring.
The Kremlin has worked aggressively to derail the EU deal by offering Kiev loans and price discounts, but also by imposing painful restrictions on some of Ukraine's exports. Ukraine has complained that the EU hasn't offered enough, but there was talk Thursday about the bloc opening its wallet further.
EU parliament President Martin Schulz said that "we, as the European Union, must ask ourselves the question what we can, and must do both economically and monetarily."
When it comes to money, he said, the EU needs "to help the people, to help the state."
EU special envoy Aleksander Kwasniewski said "the EU is ready to talk seriously about economic aid to Ukraine."
If successful in getting Yanukovych's signature in the weeks or months to come, the EU would pry Russia's historic breadbasket and a nation with huge economic potential loose from Moscow's orbit and draw it into the West's embrace. Instead, Moscow would like Kiev to join a separate union that aims to rival the EU.
"I have no hope that it will succeed this time, but the door is open," German Chancellor Angela Merkel said at the opening of the summit. "We will make very clear that the EU is ready to take in Ukraine as an associated member."
French President Francois Hollande was also planning to talk to Yanukovych on Friday to try and change his mind.
Ukraine itself also held out some hope for a deal in the near future.
"I am sure that the decision at tomorrow's summit will be positive. We will find a solution," Ukraine's first deputy prime minister, Serhiy Arbuzov, said.
Faced with pressure from Russia, Yanukovych shelved plans for closer ties with the EU last week, robbing the EU Eastern Partnership summit of its signature moment.
While facing pressure from the EU, Yanukovych is grappling with discontent at home. About 10,000 demonstrators in Ukraine's capital demanded the signing of the EU deal, the latest in daily protests since Yanukovych suspended the signature.
Popular mass protests in 2004, known as the Orange Revolution, overturned Yanukovych's fraud-marred election victory and brought his pro-Western opponent to power, and he is wary of a repeat of the same scenario now.
The protesters have been urging him to sign the EU deal and many have called for the release of jailed former Prime Minister Yulia Tymoshenko, a condition of the agreement.
Even if the EU is willing to discuss financial conditions, it will have less leeway on concessions when it comes to its cherished values of justice.
But Tymoshenko herself has urged European leaders to ink the deal with Ukraine without linking it to her release.
Tymoshenko's daughter Eugenia told The Associated Press in an interview in Vilnius that "it's not political prisoners who need to be saved now, but Ukraine needs to be saved."
Analysts believe that Yanukovych is trying to play both sides, while attempting to secure a better short-term deal with Moscow.
"The Yanukovych line at Vilnius seems to be to play for time keep options open, and come away with something which he can then use in negotiations with Russia likely next week over a gas financing deal," said Tim Ash, chief emerging-markets economist at Standard Bank in London.
"He probably hopes he can get enough 'warm words' from EU leaders in terms of the EU integration process to calm the mood on the streets, and take momentum out of street demonstrations," Ash added.
___
Follow Raf Casert on Twitter at http://www.twitter.com/rcasert
