"Romano Prodi said he was flattered, but declined the proposal to head the company," the spokesperson said after a meeting between Prodi and Gazprom's CEO, Alexei Miller.
He added that Prodi had drawn attention to progress in trade and political ties between Russia and Italy during the meeting.
Earlier on Monday, Prodi's press secretary Silvio Siriana said that the Italian premier, also the former head of the European Commission, had turned down the presidency of South Stream and that it was "highly unlikely that anything will change."
Prodi steps down in a few days to give way to media tycoon Silvio Berlusconi after his defeat in Italy's general election in mid-April.
Gazprom said in a statement that Miller had also met with Eni president, Paolo Scaroni, to discuss ongoing cooperation in the South Stream project - a pipeline expected to pump 30 billion cu m of Russian gas to Europe annually from 2012 with an estimated cost of $14 billion - and joint oil and gas projects in third countries, including Libya.
"The companies reaffirmed an interest in mutually beneficial, strategic cooperation in the energy sphere," the Russian monopoly said in a statement.
"We are satisfied with the talks with Gazprom," an Eni spokesman said, without giving further details.
The 900-km South Stream pipeline will run from Russia across the Black Sea to Europe. The Balkan nations Serbia and Bulgaria, as well as Hungary, have recently joined the project, seen as a rival to the EU and U.S.-backed Nabucco pipeline.
Italy is Europe's second largest importer of Russian gas. It also buys gas from Algeria.
In November 2006, Gazprom and the Eni group signed a deal allowing the Russian company to provide direct supplies to the Italian market. Supplies are expected to rise by 3 billion cu m a year by 2010. In 2007, the Russian monopoly supplied some 21.9 billion cu m of gas to Italy.
Gazprom also plans to launch operations in Libya with Eni after it closed a deal with the African state's National Oil Corporation to engage in upstream and downstream oil and gas production. The deal was finalized during Russian President Vladimir Putin's visit to the country earlier this month.