In an interview with Russian public television, Panagiotis Lafazanis indicated he had had a series of very productive meetings in Russia, which is ready to participate in the financing.
He said there is "enormous interest" among Greek companies for an extension of the Turkish Stream gas pipeline.
Moscow axed its South Stream gas pipeline to southeastern Europe last year, even though construction had already begun, as relations with the EU hit a nadir over Russia`s role in the Ukraine conflict.
Instead, Moscow announced a pipeline to Turkey, which should be ready in December 2016, and told European nations they would need to build links to get the gas.
Ever since the leftist Syriza party swept the elections in January, Moscow has been courting Greek Prime Minister Alexis Tsipras, a former Communist who has made no secret of his desire for closer ties with Russia, and criticised the EU sanctions imposed over Ukraine.
Tsipras is struggling to unblock EU and IMF rescue funds, and Russia has dangled the possibility it will help finance the project, which it has alluded will generate revenue that Athens could use to help pay off its mountain of debt.
"We already know that it will be a Greek public company which would be in charge and furthermore, the question of financing is already resolved: the infrastructure costs are estimated at around two billion dollars," said Lafazanis.
The minister said a deal could be reached by the three-day Saint Petersburg International Economic Forum that begins on 18 June.
Russian media have said that other countries interested in linking up the pipeline in Greece are hesitant for fear of angering the European Union.
More about:
