The Edinburgh-based practice, which is to open an office in Moscow, is working on about 20 projects in Russia, and is looking to add Gazprom's offices in St Petersburg to its list.
The project will be one of the most ambitious projects in modern Russia, and will include a 300m tower on a 4.34ha site on the banks of the River Neva in the heart of the historic city.
Tony Kettle, the UK managing director, said the firm's understanding of Russian culture would help them win the commission.
He said: 'It's understanding Russia, and really having sensitivity for the historical buildings they have. We've worked there and understand the culture and there's not many architects in the UK or really even the world that have that experience.'
RMJM is just the latest in a long list of UK-based practices scrambling for work in Russia.
One of the most high profile was Norman Foster's, whose Moscow City Towers scheme was slammed by Russian critics as being 'horrible'.
The pitch by the Scottish practice comes just months after they won the commission for the spiralling City Palace Tower, a 46-storey office retail block three miles from the Kremlin in Moscow.