Binding bids are due to be submitted on 29 May for DEPA, which posted a net profit of €106 million last year. Gazprom last year made a preliminary bid of €900 million.
Gazprom is already DEPA's main supplier, providing about 60% of its gas last year. It cut its supply prices by about 7% in 2011, but Greek energy players say prices are still high compared with what Gazprom charges in other parts of Europe with more competition.
Gazprom's chief executive Alexei Miller arrived in Athens on Tuesday for talks with Greek Prime Minister Antonis Samaras and other Greek officials. It was the third visit by senior Gazprom officials since March.
Miller sought assurances that DEPA's austerity-hit customers will settle arrears of €380 million and a concession that Gazprom will not have to deposit 20% of the purchase price as a guarantee before the sale gets European Union approval.
"The two sides discussed their exceptional cooperation in the natural gas market," Gazprom said in a statement after Miller's talks with Samaras. Gazprom also said the two sides wanted to develop their "mutually beneficial cooperation" further.
If Athens fails to sell DEPA, it will miss a target to raise €2.6 billion from privatisations this year under the terms of its international bailout. It would then need to make up the shortfall with extra austerity measures, which it is loath to do.
Greece has already agreed to reduce the required guarantee and is striving to resolve DEPA's liquidity problem, said Stelios Stavridis, chairman of Greek privatisation agency HRADF in an interview with state radio NET.
According to Greek sources close to the sale, Gazprom is concerned that the European Union might block the DEPA acquisition, in which case it would lose some of its deposit.
EU leaders are meeting today (22 May) for a special summit on energy, with security of supplies and reducing the dependence of some member countries from Russia as their main supplier featuring high in the draft conclusions.
Gazprom's only rival for DEPA is M&M Gas, a joint venture by Greek energy firms Motor Oil and Mytilineos.