Russian president Vladimir Putin and Greek PM Alexis Tsipras
The move is likely to worry the US, which has stepped up its involvement in Greece's debt talks with international creditors over fears the cash-strapped country could drop out of the single currency and come under the influence of its Cold War rival.
Panayotis Lafazanis, Greece's energy minister, said the move would be a key part of the country's "multi-faceted" foreign policy and would create 20,000 jobs, the Financial Times reported.
Figures released by Greece's National Statistics Service on Thursday showed unemployment at 25.6pc in April.
Reports in April suggested Moscow was ready to provide advanced payment to Greece for the "Turkish Stream" pipeline project, which will transport 47bn cubic metres of Gazprom's gas annualy from 2018.
Those reports were quickly denied by the Kremlin, depite Greek Prime Minister Alexis Tsipras visiting Russia to hold talks with Russian president Vladimir Putin.
During that visit to the Kremlin, Mr Tsipras insisted Greece was a "sovereign nation with the indelible right to carry out its own foreign policy".
Germany's finance minister, Wolfgang Schauble, has previously said he had no objection to any deal with Moscow, but that ultimately it would not "fix Greece's reform problems".
Beijing has also sought to invest in Greece's port infrastructure.
Mr Lafazanis, who heads up the Left Platform of Syriza, has hailed a new dawn in Greco-Russia relations and has invited the likes of state-sponsored Gazprom to drill for oil off the Greek coast.
It comes amid reports Greece's European creditors are willing to give the country debt relief, following its default on loans to the IMF last month.
I do hope, for Greece's sake, that they accept Russian and Chinese investment to kick start their Austerity-carpet bombed economy. The Banksters are too eager to slip Greece another sedative while they economically rape it.
Heavens to Mergatroid. Grexit with a big New York raspberry.