"We received an offer from Exxon. We will likely study this possibility. But we haven't make any decision today," Andrei Kuzyayev, head of LUKOIL foreign operations was quoted as saying.
LUKOIL, which is already developing West Qurna-2, has said that West Qurna-1 is "too big for it to swallow".
A LUKOIL spokesman declined immediate comment.
ExxonMobil has informed the Iraqi government it wants to pull out of a $50 billion oil project in southern Iraq.
LUKOIL is attempting to offset production decline at its fields in Russia, where it faces competition from the state-backed companies, by acquiring foreign upstream assets.
LUKOIL is active in Middle East, Central Asia, West Africa and Latin America. But Russia's vast Arctic offshore reserves are off-limits for the company due to legal restrictions, which allow only state-controlled company participation.
Doubts about who can replace Exxon in the important project could raise questions about Iraq's target to increase crude output to 5-6 million barrels per day by 2015 from 3.4 million bpd.
Some industry sources have said Baghdad is keen to replace Exxon with companies from Russia or China. But it was unclear which companies would have the financial heft to follow Exxon.
(Reporting by Vladimir Soldatkin, editing by William Hardy)
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