RIA Novosti reported the presidential bill needed 226 votes but only 147 members voted for it to be included on the agenda for a second reading.
Tymoshenko was sentenced to seven years in prison in October for abuse of office by awarding gas contracts to Russia in 2009.
The verdict has been widely condemned.
The European Union and the United States have said Tymoshenko's sentence for exceeding her authority was a politically motivated and selective use of the judicial system. Russia has also criticized the sentence as politically motivated.
RIA Novosti said Ukraine's parliament passed the first reading of a bill that would reduce sentences for some economic crimes but rejected an amendment that would have decriminalized a section of the criminal code stipulating jail time for abuse of office.
On Friday, the State Tax Service said Tymoshenko faced embezzlement and fraud charges, including concealing $165 million in corporate revenue and theft of public funds and tax evasion dating to the late 1990s, when she headed United Energy Systems of Ukraine, the main importer of Russian natural gas at the time.
The charges had been dropped under the statute of limitations.