The accords on association and free trade, due to be signed at an EU-Ukraine summit on November 28 in the Lithuanian capital Vilnius, offer the former Soviet republic the chance of an historic shift westwards away from Russia.
But signature hinges on freedom for ex-prime minister Tymoshenko, a fierce opponent of President Viktor Yanukovich.
She was jailed in 2011 for seven years for abuse of office after a trial which the EU says was political.
Yanukovich, who only narrowly defeated her in a run-off vote in February 2010, has refused to pardon her, apparently fearing she could stage a comeback and spoil his chances of re-election in 2015.
But, under pressure from the 28-nation EU bloc, he has said he will sign any draft law from parliament that would allow his adversary to go to Germany for medical treatment for severe back problems.
Pro-Yanukovich deputies, who dominate in parliament, have been haggling with the opposition over the wording of a law that would allow Tymoshenko to leave for Germany - the crux being whether she goes as a free person or as a convicted criminal.
Her parliamentary supporters hung a white banner across the speaker's rostrum, declaring "Freedom for Yulia!", and more than 2,000 people demonstrated outside calling for her release.
But deputies from the pro-Yanukovich Regions Party seemed to toughen their position.
Their faction leader referred bitterly to Tymoshenko's alleged past misdeeds and spoke of "serious differences" in their ranks about whether she should be released at all.
"There is no consensus among us about a draft law for the treatment (abroad) of convicted persons," said the faction leader, Oleksander Yefremov, though he added that efforts would continue to find a compromise.
The EU has warned the Yanukovich leadership that, with only three weeks left to the Vilnius summit, time is running out.
The wrangle over Tymoshenko's release takes place against a background of increasing tension between the ex-Soviet republic and Russia over Ukraine's westward course.
The Kremlin, which has failed to persuade Kiev to join a Russia-led customs union instead, has warned Ukraine of possible trade action in retaliation and is pressing for urgent payment of an $882 million bill for natural gas.
Two EU mediators, who have been shuttling in and out of Kiev for 18 months to nail down a deal over Tymoshenko, were set to meet Yanukovich again in Kiev later on Thursday.
'SIGN ... OR NOT TO SIGN'
Irish politician Pat Cox and former Polish President Aleksander Kwasniewski were also due to see Tymoshenko, who is in hospital under prison guard in the northern town of Kharkiv.
They are focusing their attention on a compromise under which the 52-year-old politician could travel to Berlin for treatment for her back.
Tymoshenko's supporters have now dropped their call for her to be given a "full amnesty" and say they will settle for an option under which her sentence would be automatically wiped out if she went abroad for treatment.
But this option has been opposed by pro-Yanukovich deputies.
"This is an historic moment - will Ukraine sign, or not, the agreement with the EU? We, the opposition, declare we are ready for any compromise so that Ukraine can sign, but for this Yulia Tymoshenko must be freed," Arseny Yatsenyuk, leader of her Batkivshchyna (Fatherland) party, told parliament.
The conditions attached by the Yanukovich camp to any release of Tymoshenko could bear directly on the outcome of a November 18 pre-summit meeting of EU foreign ministers to assess whether Kiev has met key democratic criteria, including ending what the bloc calls "selective justice".
The EU is split between states such as Poland, which stress the need to prise Ukraine away from Russia's embrace, and those like Sweden and the Netherlands, which argue the bloc should not compromise on principles of civil rights and justice.
Yefremov, a close ally of Yanukovich in parliament, voiced alarm that the EU, having secured Tymoshenko's release, might then decide not to sign with Ukraine.
"Once we have fulfilled all your conditions, is there from your European side any guarantees that these agreements will be signed? I have not heard any answers (to this question) apart from general talk such as 'we are 28 countries and the opinion of everyone has to be taken into account'," he said.
Source: The Star Online