World Bulletin / News Desk
Tymoshenko, 52, a former prime minister and arch rival of Yanukovich, was jailed for seven years in October 2011 for abuse of office linked to a 2009 gas deal she brokered with Russia.
The EU says her prosecution smacks of "selective justice" and Western governments say her continuing confinement threatens the signing of agreements on political association and free trade with the 27-member bloc in November.
The Yanukovich leadership says it favours European integration to forging closer ties with Moscow in aRussia-led customs union and hopes the landmark EU accords can be signed at a summit in Lithuania.
The free-trade agreement potentially on offer from the EU would open up a huge market for Ukrainian exports - steel, grain, chemicals and food products - and provide a powerful spur for much-needed foreign investment.
But freeing Tymoshenko, a fierce political campaigner, and lifting other pending charges against her could be risky for Yanukovich as he prepares to run for a second term in 2015.
Releasing her to travel to Germany to receive medical treatment for chronic back problems has emerged as a possible formula which would improve Yanukovich's standing with the EU.
After meeting EU officials in Kiev on Friday, the three main opposition leaders urged Yanukovich to accept the offer.
"If Tymoshenko is able to travel (to Germany) and get an emergency operation this will be enough for the European Union to consider the reality of signing this agreement (on association)," one of the leaders, former economy minister Arseny Yatseniuk, told reporters.
"We expect a decision from the President giving Yulia Tymoshenko the chance of receiving medical help abroad," he said.
Tymoshenko was a major player in the 2004 Orange Revolution protests that doomed Yanukovich's first presidential bid. She later ran him close in a bitterly fought run-off vote in February 2010.
Despite pressure from Western governments and the opposition at home, there has been no sign of the authorities relenting in her prosecution.
Since she was jailed for alleged abuse-of-office in 2011, she has been charged on further counts of embezzlement and tax evasion and the authorities have also been investigating her for alleged involvement in the contract murder of a powerful businessman in the 1990s.
She has denied all the charges against her.