"I'd like to train here but if we don't have the right conditions I shall be forced to train elsewhere," Baiul told a news conference.
Baiul, 16, has become a national heroine since capturing the Olympic crown in Norway last month, a day after suffering back and leg injuries in a collision with another skater during practice.
She defeated American Nancy Kerrigan for the title, giving Ukraine its first gold medal as an independent state.
She told reporters she decided to miss this week's world championships in Japan because her back still hurt.
Baiul has received several offers to train abroad since her Olympic triumph -- earlier this month she and former Olympic champion Viktor Petrenko appeared ready to move to Connecticut to train. This prompted President Leonid Kravchuk to issue orders to upgrade her facilities in Odessa. Kravchuk took Baiul with him on a visit to the United States.
Baiul's coach Galina Zmiyevskaya said the skater would be very sorry to leave Ukraine but might have little choice.
"She has never wanted to stay in another country and compete under another flag and this probably will never happen," she said. "But I do not rule out the possibility of training overseas. Our sports palace is in a dreadful state. There has been no refurbishment for 19 years. We have to clear the ice and lay it down ourselves. The cooling plant breaks down, the ice melts. But Oksana is, was and will be a Ukrainian athlete."
She said Baiul had received offers to train from countries as distant as Brazil.
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