The investigation was sparked by a report from Russian media reports on 28 January quoting former Federal Security Service (FSB) chief Nikolai Kovalyov as saying two British citizens have been arrested and that "they are not silent, they are talking."
Reuters on 28 January quoteed a spokeswoman for the FSB as neither denying nor confirming the report.
The reports come after Russia this week accused Britain of running a spying operation in Moscow.
(Sky News, Interfax, Reuters)