Yanukovich is on the run after being toppled by bloody street protests in which police snipers killed demonstrators.
An advisory from the Treasury's Financial Crimes Enforcement Network (FinCEN) said that U.S. financial institutions "should be aware of the possible impact that public reports of high-level corruption by senior members of the Yanukovich administration and other illicit activity by members of the administration may have on patterns of financial activity".
FinCEN said it was reminding banks they were required to apply "enhanced scrutiny" to accounts held by Yanukovich or his circle "and to monitor transactions that could potentially represent misappropriated or diverted state assets".
Ukraine's parliament voted on Tuesday to send Yanukovich to the International Criminal Court over police violence against protesters which it said had led to the deaths of more than 100 citizens of Ukraine and other states.
The country's new leaders have appealed for urgent international aid, saying it needed $35 billion over the next two years. Acting President Oleksander Turchinov warned that Ukraine was close to default and "heading into the abyss".