The Iraqi government, however, hasn't signaled a reversal of opinion that the deal was canceled prior to Saddam's overthrow, thus no longer valid.
Lukoil, Russia's largest private oil company, is hoping to develop the West Qurna oil field under a 1997 deal. Russia claims it was frozen in 2002; Iraq says it was canceled due to non-performance.
Vagit Alekperov, Lukoil's chief executive officer, is in Iraq now, meeting with top government officials and those in the Oil Ministry. In a statement quoted by RIA Novosti and other media outlets, Lukoil said the company and Iraq will form a working group to bring the deal in line with the current Iraq government.
Chevron and Total, however, are in talks currently with the ministry for a two-year Technical Support Agreement for West Qurna. The firms would be paid to provide expertise, training and equipment to increase production by 100,000 barrels per day.
And while that wouldn't guarantee it wins an expected bidding round in coming years for longer-term investment, the ministry admits the more knowledge a company has of the field the better its bid will be.
Iraq is to offer an unspecified number of fields for development tenders later this year. West Qurna is reportedly not among them.
In a statement, Lukoil also said it "will take part in tenders for new projects to be announced by the Iraqi government after it has adopted a new law on oil."
Putin, in a letter to Prime Minister Nouri al-Maliki, also pressed for a Russian deal to rebuild an Iraq-Syria oil pipeline. Last month Russia wrote off $12 billion in Saddam-era debt with no direct strings attached. The debt relief had been used in the past as an offer for revising the West Qurna deal.
"The documents signed at the session of the Russian-Iraqi commission on trade, economic and scientific cooperation and the intergovernmental agreement on settling the Iraqi debt to Russia on credits provided earlier are, in our view, a good basis for intensification of partnership relations," Kommersant reports Putin's letter stated in part.
West Qurna contains up to 21 billion barrels of proven reserves, according to the U.S. Energy Department's data arm, the Energy Information Administration. Iraq's total proven oil reserves are 115 billion barrels.
Notable deaths of 2014 [PHOTOS]