Eni discovered the supergiant offshore gas field in August 2015 and recently ran its first successful production test at the asset, which is the largest gas discovery ever made in the Mediterranean.
Citing industry sources, the Italian Insider website reported that Lukoil is preparing to acquire a 20 per cent stake in the fields operating company.
Production is expected to begin by the end of 2017. The project is valued at $5.6bn, but the investment in the fields will amount to $13bn, according to Eni.
The administrative director of Eni, Claudio Descalzi, has said on several occasions that the company is planning to partner with another company to operate Zohr, according to the Italian press.
Enis shares on the Milan Stock Exchange increased by around 1 percentage point to reach $15.13 after the Italian press reported on the alleged Lukoil deal.