Mr Yanukovych has built a majority in parliament, with the help of communists and socialists.
Opposition leader Mr Yanukovych said any new coalition should include his Party of the Regions.
Mr Yanukovych's backers say the constitution bans him from interfering with an independent judiciary.
Mr Yanukovych is already talking of changing the law to decriminalise Ms Tymoshenko's alleged offence.
In Ukraine, Mrs Clinton told President Viktor Yanukovych that the door to potential Nato membership remained open.
According to the official election result, Mr Yanukovych won with 49.46% of the vote against Mr Yushchenko's 46.61%.
Ms Tymoshenko leads the second largest group in the 450-seat assembly, after Mr Yanukovych's Party of the Regions.
There was no mention of Tymoshenko in the decree Yanukovych signed on Sunday.
FORBES: Ukraine's President Sets Political Prisoner Free to Please The West
Her coalition was unable to overcome opposition from former Prime Minister Viktor Yanukovych.
However, Mr Yanukovych won the last presidential election, in 2010, defeating Mrs Tymoshenko.
Tensions have been running high since then, with Mr Yanukovych and his allies disputing the president's authority to do so.
He has not publicly withdrawn support for Yanukovych but if he does, it may shake up an already competitive race.
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Clearly Europe is tired of Ukraine but president Yanukovych has made it clear that Ukraine is sick of Europe, too.
Ukraine President Viktor Yanukovych said a special investigation team will be set up to probe the explosions, the news agency reported.
The world should pay close attention to the imminent election of Viktor Yanukovych, a pro-Russia candidate running for president of Ukraine.
Ukraine's Vice Prime Minister Hrihoriy Nemyria, a member of Ms Tymoshenko's bloc, denied the party was trying to form a coalition with Mr Yanukovych's party.
Tymoshenko, a fierce rival of president Victor Yanukovych, is serving a seven-year jail sentence for abuse of office and faces another trial on tax evasion charges.
She accuses Mr Yanukovych of exacting political revenge on her.
BBC: Tymoshenko case: Europe pressure on Ukraine intensifies
However, three weeks later the President Yanukovych signed a decree instructing ministers to come up with a new budget providing medical care for people living with HIV and Aids.
President Viktor Yanukovych - elected in April 2010 - has said EU membership is a "strategic aim" but has been accused of being a placeman for pro-Russian tendencies in the country.
Mr Yanukovych currently controls about 250 seats in parliament.
Ms Tymoshenko, a former prime minister and key rival of Ukraine's President Viktor Yanukovych, is serving a seven-year jail sentence for abuse of office and faces another trial on tax evasion charges.
BBC: Tymoshenko case: Europe pressure on Ukraine intensifies
While Mr Yanukovych has given no comment on the threats of European leaders as significant as Germany's Chancellor Angela Merkel to boycott the tournament, Ukraine's foreign affairs ministry has been open in its condemnation.
She has said the charges of abuse of power are a tissue of lies, inspired by the man she helped oust in 2004, Viktor Yanukovych - who returned to defeat her in the 2010 presidential election.
Tymoshenko, who was a leading figure in the 2004 Orange Revolution and had been on a 20-day hunger strike until last week, argues she has been victim of mistreatment and politically-motivated imprisonment driven by current president Viktor Yanukovych.
It is a bitter reversal for Tymoshenko since the Orange Revolution days, when she and her ally Viktor Yushchenko packed the streets of Ukraine in protest at a rigged election that went in favour of the pro-Russian Mr Yanukovych.
The problems between the billionaire and his candidate may help sway the election to Serhiy Tihipko (or Russian spelling, Sergiy Tigipko), ahead of both Yanukovych and one-time Orange Revolution darling and Forbes Power Woman Yulia Tymoshenko, who is also a candidate.
FORBES: Ukrainian Billionaire and His Presidential Candidate
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