Chancellor Angela Merkel is considering such a boycott, the German news website Der Spiegel reports.
Environment Minister Norbert Roettgen said the government should stay away from Ukraine during the tournament. Ukraine is co-hosting it with Poland.
Ms Tymoshenko says she is very ill.
She is reported to be on hunger strike and on Friday images appeared showing bruises on her body, which she says prison guards inflicted. She is being held in Kharkiv, eastern Ukraine.
An official in the Ukraine Prosecutor's Office, Vadim Goran, denied her allegation, saying the bruises came from "pushing against blunt, hard objects, or banging into them" and "in no way resulted from a punch to the stomach as she says".
After seeing the photos Sweden's Foreign Ministry summoned the Ukrainian ambassador and demanded an explanation.