* Other European utilities have renegotiated with Gazprom
* Eni one of Russia's biggest gas customers
* Investment decision on South Stream expected Nov. (Releads, adds context, shares)
By Svetlana Kovalyova and Stephen Jewkes
MILAN, March 1 (Reuters) - Gazprom has agreed a revamp of its long-term gas supply contracts with Italy's Eni in a move showing the Russian giant's willingness to make concessions on gas price and supply terms to maintain relations with key European customers.
Russia currently supplies Europe with more than a quarter of its gas needs, a share expected to grow further as falling production from maturing fields in the North Sea increases Europe's reliance on imports.
Many utilities have asked for concessions from Gazprom after booking multi-billion euro losses in 2011 due to very high long-term contract prices compared to spot prices.
Germany's E.ON, Austria's OMV and Italy's Edison have already drawn concessions from Gazprom while France's GDF is in talks.
"All these contracts have renegotiation clauses. And we don't know the details yet. But the fact that Gazprom hasn't stonewalled Eni points to a willingness to reach friendly deals with its main European partners," a gas industry source said.
Eni is Russia's biggest gas customer. Its Chief Executive Paolo Scaroni said last month the renegotiation of contracts with Gazprom would be retroactive for 2011.
"The agreement on the revision of the price of the gas supply contracts represents an important step in the forty-year long strategic partnership between Gazprom and Eni," Eni said in a statement on Thursday.
Sources close to the matter said on Thursday the effect of the renegotiation will be booked in the first quarter of 2012.
Gazprom has said it expects to grab increasing share of the European market, rising from 27 percent last year to 30 percent by 2020 and to 32 percent by 2030.
Russian Prime Minister Vladimir Putin has hinted change may be afoot for Gazprom, saying in February there would be a transition for Gazprom to work under a "different regime".
The European Union is keen to find new sources to diversify supplies for energy security reasons.
Its long-delayed Nabucco pipeline aims to cut reliance on Russian gas by bringing 10 billion cubic metres (bcm) a year of Caspian gas to western Europe.
In its statement Eni said it and Gazprom expected to make the final investment decision on the South Stream gas pipeline project in November and start the pipeline construction by December 2012.
South Stream, a rival to European-backed pipeline projects to ship gas from the Caspian region, is expected to export around 63 bcm to southern Europe starting from 2015 bypassing Ukraine. It is estimated to cost more than 15 billion euros.
Gazprom owns 50 percent of the South Stream project. Italy's Eni has 20 percent, and France's EDF and Germany's Wintershall each own 15 percent.
Eni shares closed up 1.6 percent at 17.6 euros while the European oil and gas index was up 0.91 percent. (Editing by William Hardy and Mark Potter)