The proposal was submitted to President Vladimir Putin by lawmaker Andrei Krutov, a member of Spravedlivaya Rossiya Party.
According to Krutov, the measure will have a positive effect both for Greece and Russia. He added that the cooperation between the two countries would be developed through supranational institutions, including the Eurasian Economic Union, the Shanghai Cooperation Organization and BRICS.
"Greece is a reliable partner for Russia. Between 2010 and 2013 trade between the two countries doubled," according to the document.
In addition, Krutov underscored that Russia and Greece are not only economic partners, but also have much in common in their mentalities because Greece is among the few Orthodox European countries.
In early-April, Russian Agriculture Minister Nikolai Fedorov said the government was ready to discuss the removal of the food embargo for certain countries.
According to experts, if the embargo is lifted from Greece it would help Russia develop its energy projects in Europe.
"It would help Russia carry out its energy projects, especially the construction of the Turkish Stream gas pipeline on the Greek territory," said Konstantin Korischenko from the Russian Academy of National Economy and Public Administration.
In August 2014, Russia introduced a one-year ban on imports of many food products from the US and the European Union. The move was made in response to economic sanctions adopted by the West against Russia over the country's alleged interference in the Ukrainian crisis. Moscow considers the accusations to be groundless.