The energy company, which is the world’s biggest gas producer, is understood to be interested in appointing an agency partner in the UK. It has contacted London shops to arrange meetings.
Gazprom’s most high-profile marketing activity is its sponsorship of the Uefa Champions League. Campaigns have included animated TV idents that end with the line: "We light up football."
The company would represent a controversial client for UK agencies. European states have implemented sanctions against Russia because of its role in the crisis in Ukraine.
Gazprom has a market value of about $77 billion (£47.8 billion). At its peak in 2007, the company was worth $360 billion.
Gazprom had not responded to a request for comment by the time of publication.