Romanov is suspected of embezzling £12 million ($18.5 million) from Lithuanian bank Ukio Bankas, where he was a majority shareholder. An international arrest warrant was issued for the Russia-born, Lithuania-based businessman four weeks ago.
Romanov, who bought a majority stake in Hearts in 2005, is believed to be in Russia.
Lithuania's central bank placed restrictions on the operations of Ukio Bankas in February, citing irregularities.
Hearts, which went into administration last month, owes £15 million ($23 million) to Ukio Bankas and the bank's administrator has warned he could seek to liquidate the Scottish club.