Roskomnadzor, the Russian communications regulator, has repeatedly sent inquiries to Google asking them to direct their citizens' web searches through an official filtering system.
A law passed in Russia last year stipulates that search engines must be connected to the federal information system (FGIS) so that the Kremlin can censor the websites that its citizens can access.
It is not clear if the system could also be used to monitor users.
Roskomnadzor spokesman Vadim Ampelonsky told the Russian news agency Interfax that the regulator does not record any information about citizens' search results.
Google was fined 500,000 rubles (£ 5,800) in December for failed search links to the filtering systems. At the time, the company neither commented nor challenged the fine.
Ampelonsky told Interfax that the company would face a fine of no more than 700,000 rubles (£ 8,100) in the event of continued infringements, which is actually less than 0.00001% of its parent Alphabet's annual turnover.
Domestic Internet companies such as Yandex, Sputnik and Mail.ru have met the requirement to connect to FGIS.
According to Interfax, if Google has alleged a "malicious non-compliance" with its obligation to associate with the FGIS, the Kremlin could consider laws that block the company in the hardest circumstances.
Google has not responded to repeated requests from Sky News for an opinion.
The regulators' aggression follows reports that Google plans to launch censored version of his search engine in China, where it is currently prohibited.
Google effectively left China in 2010 when it criticized the censorship and surveillance activities in Beijing, and Soviet-born co-founder Sergey Brin condemned the "authoritarianism" forces in the country.
Although there are few signs of a withdrawal of authoritarianism in China or Russia, the company in these countries is pleased with the Chairman of the Board, Sundar Pichai.
Mr. Brin is now the president of Alphabet and has not commented on the censored search project in China. Instead, he decided to criticize the leaks at a reported meeting with employees.