Timur Suleimenov, EEC Member of the Board for Economy and Financial Policy, told Norway's Finansavisen newspaper that the organisation would welcome Norway's involvement, but that nothing would happen in the near future.
"We would like to have Norway as a member. However, it should be emphasized that we just have made Armenia and Kyrgyzstan members, and we have no immediate plans for expansion," he said.
After The Local Norway first published this story, the EEC issued a press release stressing that the question of Norway's accession to the EEU was "hypothetical", and that it would be incorrect to describe it as an invitation.
The EEU is an economic union of Russia, Kazakhstan, Belarus, Armenia and Kyrgyzstan formed in 2014 and by many viewed as a competitor to the EU.
It was the application by the then Ukrainian president Viktor Yanukovych to join the EEU as an observer, abandoning an association agreement with the European Union, which led to the massive protests on Kiev's Euromaidan square.
The protests ended with Yanukovych being ousted from the presidency, and then Russia's annexation of Crimea in March 2014.
The conflict in Ukraine has since escalated between pro-Russian insurgents and Ukrainian troops in a number of regions.
Although Norway is not a member of the EU, it is a member of the European Economic Area and a Nato member.
Norway has along with countries in the EU imposed economic sanctions on Russia in the wake of the Ukrainian crisis.
Kazakhstan-born Suleimenov says that there is no inherent conflict between the EU and the EEU.
"I understand that you can have that impression regarding Ukraine, and with regards to other countries that are members, to some extent," he said. "But when it comes to economic development, trade, and investment, we primarily want peaceful co-existence."