"We have the ability to host the European Olympic Games. If Russia is entrusted with this, we can do it in 2023," the source said.
The European Olympic Committees (EOC) Executive Committee said in January the host would be announced by the end of the year, adding that talks were being held with several countries.
The 2019 European Games will be held in the Belarusian capital of Minsk.
In July, Russian President Vladimir Putin said that some Russian cities could potentially host the Summer Olympic Games in the future but no relevant bids have been submitted yet.
Additionally, Vladimir Dzhabarov, the first deputy head of the Russian upper house's International Committee, has said that St. Petersburg and the southern city of Sochi were ready to host the sporting event since they already had all the necessary infrastructure for it.
In 2020, St. Petersburg will host several UEFA Euro matches. The city was a host of several games during the recent FIFA World Cup. Sochi, in turn, hosted the 2014 Winter Olympics.