Greek Prime Minister Alexis Tsipras discussed energy cooperation with Russian President Vladimir Putin in a telephone conversation on Thursday, the premier's office said in a statement.
A key topic was the Turkish Stream gas pipeline from Russia to Turkey, which Greece would like to see extended to its territory.
Tsipras "reiterated that the Greek government was ready to participate, via a public company" in the construction of the gas pipeline in Greece, the statement said.
It added that Putin expressed "his intention to support a financing plan for the Greek company that would build the pipeline."
The Kremlin issued a statement confirming that "Russia was ready to study the question of financing Greek public or private companies which participate in the project."
Greece's leftist prime minister visited Moscow in early April, and Putin at the time expressed the possibility of common infrastructure projects with Greece, alluding to the potential revenue that could be used by Athens to help pay off its mountain of debt.
Tsipras, a former communist who is struggling to unblock EU and IMF rescue funds, has made no secret of his desire for closer ties with Russia and criticised the EU sanctions imposed on Moscow over the conflict in Ukraine.
He is scheduled to return to Moscow for an economic forum on June 18-20.
Russian energy giant Gazprom announced Thursday that the Turkish Stream pipeline would start operating in December 2016.
The pipeline is designed to offer an alternative to shipping Russian gas via Ukraine.
It replaces a scrapped plan to build a South Stream pipeline under the Black Sea to Bulgaria, to supply southern Europe while skirting Ukraine.
Putin axed the South Stream plan in December as relations with Brussels nosedived over Moscow's actions in Ukraine.