The 28-member bloc wants Yanukovich to free Tymoshenko, his fiercest critic, from a seven-year jail sentence which followed a trial for abuse of office he says was politically motivated.
There was no immediate word on Yanukovich's reaction to the formal request made on 4 October from the two envoys, former Polish President Aleksander Kwasniewski and Irish politician Pat Cox.
But Tymoshenko, a former prime minister, indicated publicly for the first time she was ready to accept an offer to go to Germany, though she told Yanukovich she would not give up the fight against his "dictatorship".
The EU has been pressing for her release as a condition for signing deals on association and free trade with the former Soviet republic at a summit in Vilnius, Lithuania, on November 28 and 29.
Serhiy Vlasenko, Tymoshenko's lawyer, told reporters that the two European parliament envoys had submitted the request for a pardon to Yanukovich on Friday.
Tymoshenko, a fiery politician known for her trademark peasant-braided hair, was a leading light in the 2004-5 Orange Revolution street protests that doomed Yanukovich's first bid for the presidency. She later ran him close for the presidency in February 2010 after a bitter campaign.
Following a 2011 trial which the West said smacked of "selective justice", she was jailed for abuse of office linked to a gas deal which she brokered with Russia as prime minister. The Yanukovich government says the deal saddled Ukraine with an exorbitant price for Russian gas supplies.
She is still seen as a formidable opponent who could endanger Yanukovich's bid for re-election in 2015 if she became politically active again.
Despite pressure from the West and his desire for agreements with the EU which will take his country out of Russia's sphere of influence, Yanukovich has stalled on releasing her, saying he has no powers to over-rule the courts.
Behind-the-scenes efforts to secure her release have hinged on Yanukovich's aim of ensuring she is neutralized as a political opponent once she is out, EU officials say.
In a statement released from the hospital in the northern town of Kharkiv where she is under prison guard, Tymoshenko, 52, signaled she was ready for a deal now that would take her to Germany.
German doctors have treated Tymoshenko in Kharkiv for back trouble and the Berlin government has offered her further treatment as a way out of the wrangle over her release.
"I believe that this step will ease the situation on the eve of the summit of the Eastern Partnership," she said, referring to the top-level EU meeting in Vilnius when the key agreements are to be signed.
"For the sake of a successful Vilnius (summit) and successful Ukraine, for the sake of a historic and crucial, agreement with the EU, I am ready to accept this proposal," she said.
But, using far from conciliatory language that will only grate on Yanukovich, she signaled she would continue to fight him and would not seek asylum in Germany - something which would put her out of the running politically.
"I am stating distinctly and clearly: my possible departure for Germany does not amount to emigration. I will never, anywhere, ask for political asylum. I will not hide abroad. I have long since gone beyond the point of being afraid," she said.
She accused Yanukovich of seeking to build a "European" Ukraine "on the basis of dictatorship, clientelism, corruption and political repression".
"I will actively take part in freeing Ukraine from dictatorship," she declared.