Yanukovych's comments came as pressure mounted on Ukraine from the European Union to release the 2004 Orange Revolution leader on the seventh anniversary of an uprising that had brought both her and other pro-Western figures to power.
The president said he discussed Tymoshenko with his health and interior ministers in the wake of reports that severe back pain was keeping her bed-ridden during her rounds of interrogation on yet another set of charges.
Yanukovych said that "the healthcare system (in prison) has not yet reached the sufficient standards. That is why in this case the care must be given in medical establishments in Kiev" outside the prison.
"This is likely to be done today or tomorrow," he added.
Ukraine's rights ombudsman Nina Karpacheva had earlier said her unannounced visit to Tymoshenko on Sunday confirmed that Tymoshenko's condition was "extremely serious" although she did not give further details.
Tymoshenko was first placed under arrest on August 5 before she was sentenced to seven years in jail on October 11 for abuse of authority for agreeing gas contracts with Russia in 2009.
She has insisted that her prosecution was ordered by her arch-foe Yanukovych following the Orange team's defeat in last year's presidential polls.
The process angered the European Union and dented Ukraine's hopes of one day joining the bloc.
The fate of a December summit with Ukraine concerning its future membership now hangs in the balance.
Visiting Lithuanian President Dalia Grybauskaite told Yanukovych that she had been authorised by the European Commission -- the EU's executive arm -- to warn Ukraine it could not continue with its current behaviour.
"The dominant view in Europe is that Tymoshenko and her colleagues have been victims of a political neutralisation campaign," Grybauskaite said.
The renewed EU pressure on the cautiously Russia-friendly Yanukovych came as Ukraine marked the anniversary of the 2004 Orange Revolution.
The spontaneous pro-Western rallies overturned the results of a rigged presidential poll and spawned hope of a new European future for the country under president Viktor Yushchenko and his then ally Tymoshenko.
The spontaneous demonstrations began a day after the authorities handed a controversial runoff election victory to Yanukovych despite strong suspicions that the vote actually went Yushchenko's way.
He decisively won a third round of elections held on December 26, 2004.
Tuesday's anniversary was marked by police banning all rallies and putting barriers around the main Independence Square -- also known as Maidan -- that formed the heart of the street resistance movement.
Officials explained their decision by the scheduled installation of a huge fir tree for New Year's celebrations.
But the Orange movement has failed to generate much public interest of late amid a general sense of voter frustration with politics.
Most rallies in support of Tymoshenko only drew her own party members and a small group of hardcore supporters while failing to register nationwide.
Tymoshenko herself issued a statement from jail admitting that the hopes of many had not been fulfilled by the endlessly-infighting Orange government.
"I have a mixed sense of pride for my country and guilt for the unfulfilled dreams," she said.
Former president Yushchenko however said he felt the current times in Ukraine were similar to those he encountered in the run-up to the 2004 presidential polls.
"We are now facing the same challenges as the ones that caused Maidan in 2004 -- state authoritarianism, violation of the rights of citizens and entrepreneurs ... and blatant preparations for falsified elections," Yushchenko said in an apparent reference to 2012 legislative elections.