Most of Russia's €210bn (£185bn; $245bn) worth of assets in the EU are held by Belgium-based organisation Euroclear, and so far Belgium and some other members of the bloc have said they are opposed to using the cash.
Without a boost in funding, Ukraine's finances are set to run dry in a matter of months.
Russia has warned the EU against using its money, and has filed a lawsuit against Euroclear in a Moscow court in a bid to get its money back.