The minister, Guido Westerwelle, met Yanukovich in Kyiv for more than two hours for what he described as "constructive and intensive" talks.
But Yanukovich appeared to have given no firm answer to a European Union request for him to pardon his arch-foe and allow her to leave for Germany to receive medical treatment
Tymoshenko, a former prime minister who ran Yanukovich close in a presidential election in February 2010, is now serving a 7-year sentence for abuse of power.
But the EU says she is the victim of political maneuvering and would like her to be released before it signs landmark deals on association and free trade with the ex-Soviet republic in late November.
Westerwelle told journalists after his talks that he sensed "serious attempts and serious efforts" were under way to overcome the Tymoshenko issue.
He said he had put forward Germany's proposal to receive Tymoshenko, who has back trouble, for medical treatment in Berlin as a humanitarian solution to the problem.
"We are in complicated [negotiations] from both a political and judicial point of view," he said.
Yanukovich, the opposition says, fears Tymoshenko could make a comeback and challenge him in his bid for re-election in 2015, but at the same time wants to sign deals with the EU which will help pull Ukraine out of the orbit of Russia, its former imperial ruler.
He has said he is powerless to overrule the Kiev court which found her guilty of abuse of office linked to a gas deal with Russia that she brokered in 2009. The government says the deal saddled Ukraine with an exorbitant price for gas.
Ukrainian Foreign Minister Leonid Kozhara, standing alongside Westerwelle, said Tymoshenko's release had to be in accordance with the country's constitution and laws.
He said it also represented a political problem "since millions of people in this country sincerely believe that Mrs Tymoshenko carried out a crime which was confirmed by a Ukrainian court".