Relations between the European Union and Ukraine have soured since Tymoshenko's jailing and Sweden is to join forces with Poland in a new bid to get her free and ease tensions.
Bildt and his Polish counterpart, Radoslaw Sikorski, are to meet Ukraine's richest man, Rinat Akhmetov, to try to put pressure on President Viktor Yanukovich to bring about the release of his political rival, Reuters reported.
The trio are set to meet at a Champions League football match in eastern Ukraine on Wednesday.
Tymoshensko, who is a former prime minister, was sentenced to seven years in prison in October on charges of abusing her office.
She remains in custody pending appeal and maintains that the charges are a result of a political vendetta.
The EU has dismissed the trial of Tymoshenko as a having a political motive and issued warnings that Ukraine progress towards a closer partnership with the union has been put in jeopardy.
Bildt confirmed on his blog that he is to travel to Ukraine to watch the match at the new Donetsk stadium.
"But if the truth be known it is not football which is the main purpose of the trip, but to take the temperature of the political development in this important part of Ukraine," Bildt wrote.