Putin said Thursday it would "be our pleasure" to host Tymoshenko, Ukraine's former prime minister, who is serving a seven-year sentence for overstepping her official authority, The New York Times reported Friday.
Ukrainian officials rejected Putin's proposal.
German officials extended a similar offer.
Tymoshenko went on a hunger strike April 20 to protest alleged mistreatment. She said guards punched her while she was being taken to a prison hospital for back pain.
A Ukrainian judge delayed the start of Tymoshenko's second trial until May 21, citing health concerns resulting from her hunger strike. The trial is on charges she evaded taxes while heading an energy company in the 1990s.
Putin said concerns raised by Western countries and human rights groups about the Tymoshenko case should not affect the Euro 2012 soccer tournament, which several European countries said they would boycott.
"In absolutely every case, you can't mix politics, business and other issues with sport," Putin said. "Sport is outside politics."