"We are counting on Ukraine’s return to the integration process,” presidential advisor Sergei Glazyev told an economic conference in Moscow.
The Eurasian Union, to which Glazyev was referring, is an association of former Soviet countries that is due to be launched in 2015.
Street protests in Ukraine were sparked last year by the President Viktor Yanukovych's decision to reject closer economic ties with the European Union and increase trade links with Russia instead.
Demostrators in the former Soviet nation, who still occupy the center of the capital, Kiev, caused the fall of the government last month and are demanding that the country turn away from Russia and sign trade deals with the EU.
Glazyev had previously warned Ukraine that it would be "suicidal” to go ahead with EU integration. Ukraine received financial assistance worth $15 billion from Russia after it declined to sign the agreements with the EU.
The Moscow-led Customs Union, which currently includes Belarus, Russia and Kazakhstan, is seen as a precursor to the Eurasian Union. Russia would also like to see Ukraine join the Customs Union.
Then-US Secretary of State Hillary Clinton said in 2011 that both projects were attempts to "re-Sovietize” the region, and warned that the United States would oppose them.