Russian communications regulator Roskomnadzor has sent repeated requests to Google requiring it to route its citizens' web searches through a government filtering system, according to reports.
A law passed in Russia last year requires search engines to be connected to the federal state information system (FGIS) allowing the Kremlin (IOB: 0Q8D.IL - news) to censor the websites which its citizens can access.
It is not clear whether the system could also be used to conduct surveillance on users.
Roskomnadzor spokesman Vadim Ampelonsky told Russian news agency Interfax that the regulator did not record information on citizens' search results.
Google was fined 500,000 rubles (£5,800) in December for failing to connect Search to the filtering systems. At the time the company neither commented on nor appealed against the fine.
Mr Ampelonsky told Interfax the company faced a maximum fine of 700,000 rubles (£8,100) in the case of continued violation - effectively worth less than 0.00001% of the annual turnover for its parent company Alphabet (Xetra: ABEA.DE - news) .
Domestic web firms in Russia including Yandex, Sputnik and Mail.ru have complied with the requirement to connect to the FGIS.
According to Interfax, if Google was deemed to have conducted "malicious non-fulfilment" of its obligation to connect to the FGIS, the Kremlin may consider legislating to block the company in the most severe circumstances.
Google did not respond to Sky News' repeated requests for a statement in response.
The regulator's aggression follows reports that Google is planning to launch a censored version of its search engine in China, where it is currently banned.
Google effectively left China in 2010, when it criticised the censorship and surveillance activities of Beijing, and the company's Soviet Union-born co-founder Sergey Brin decried the "forces of authoritarianism" in the country.
Although there is little sign of authoritarianism receding in either China or Russia, the company is content operating in those jurisdictions under chief executive Sundar Pichai.
Mr Brin is now the president of Alphabet and has not spoken out regarding the censored search project in China, instead choosing to criticise the leaks during a reported meeting with employees.