Greek Foreign Minister Nikos Kotzias has met with his Russian counterpart Sergei Lavrov in Moscow as Prime Minister Alexis Tsipras attempts to reform Athens' bailout programme with the EU.
Speculation has grown that Greece's radical left wing government could turn outside the European Union in a bid to relieve the pressures of austerity on the Greek economy.
The timing of the invitation is sure to rile European leaders, who are currently at odds with Russia over the ongoing conflict in Ukraine.
Both Russia and China have offered economic support to Athens, the country's deputy foreign minister said on Tuesday (10 February), although Greece had not requested this assistance, he added.
But Panos Kammenos, head of the country's junior coalition partner, has said Athens could seek help from Russia or China if Tsipras failed to clinch a deal with European leaders.
Athens' bailout agreement with the EU is set to end on 28 February and its leaders have vowed to renegotiate the terms of any new deal.
European leaders have warned that Athens would not be able to renege on the bailout conditions ahead of Wednesday's talks.