Lukoil said the contract could be worth as much as $100 million, reports Russia's state-run news agency RIA Novosti. The company said the contract should be signed next month.
Norwegian energy company Statoil worked with Lukoil in 2009 after winning a competitive bid for the West Qurna-2 oil field in southern Iraq. Project partners had expected a production level of 1.8 million barrels of oil per day by 2017.
Statoil transferred its 18.75 percent stake to Lukoil early this year.
Iraq has the fourth-largest oil reserves in the world. A report from the International Energy Agency this week said Iraqi oil production could more than double by 2020 and it could eventually pass Russia as a major oil exporter.
The IEA warned, however, that "success is not assured." Development is complicated by legal rows between the Kurdish government and the central government in Baghdad.
The Lukoil announcement came as Iraqi Prime Minister Nouri al-Maliki met in Moscow with Russian leaders.