Russian representative on the Eurasian Economic Commission board Andrey Slepnev said the proposal was approved by all members of the panel during an expert-level meeting held in the Armenian capital, Yerevan.
The EEU is an economic union of former Soviet states led by Russia to guarantee free transit of goods, services, capital and workers among members.
Speaking to reporters, Slepnev described Iran as “our key partner in the Middle East” and underlined its rising weight given that “the prospects of lifting international sanctions is now more real than ever".
“In this respect, our long-term expectation of development of economic ties with Iran and expectation of its economic growth is definitely a serious ground for a free trade agreement between EEU and this country," the Russian news agency TASS quoted him as saying.
Slepnev said EEU was also in free trade agreement talks with Egypt, Israel and Vietnam, China’s Xinhua news agency reported.
China and India have already indicated their interest in joining a free trade zone with the Eurasian Economic Union.
Slepnev called China a “very important trade and strategic partner” for EEU, saying free trade talks with the country would begin soon.
"We have discussed economic cooperation with the Chinese side and soon we will start negotiations on the issue," Xinhua quoted him as saying.
At its current capacity, the bloc has a combined population of 170 million people and a gross domestic product of $2.7 trillion.
It unites Russia, Belarus, Kazakhstan and Armenia, with Kyrgyzstan becoming the latest member.
The bloc which began functioning on January 1, 2015 is being tipped as a major economic force to challenge the might of the European Union and the US.
Russian President Vladimir Putin has also called for a regional currency union, saying it would make "easier to react to external financial and economic threats and protect our joint market".
The Russian leader, however, did not outline a timeframe and experts have said the initiative would take years of planning which required collaboration on monetary policy.
The Russian ruble has lost around 40% of its value under falling oil prices and economic sanctions imposed by the United States and the European Union over the Ukraine crisis.
