A former sports minister, Mr Tyagachyov was appointed in 2001
There are reports that the head of Russia's Olympic Committee has stepped down after the nation recorded its worst performance at the Winter Games.
A committee spokesman said Leonid Tyagachyov hade decided to resign after Russia finished with just three golds in its 15-medal haul from Vancouver.
Mr Tyagachyov's own spokesman, however, said such reports were premature.
Russian President Dmitry Medvedev had on Monday called on Russia's senior sports officials to resign.
He likened sports bureaucrats to "fat cats".
The 2014 Winter Olympics are to be held in Russia's Black Sea resort of Sochi.
The Itar-Tass news agency quoted a spokesman for the Olympic Committee as saying Mr Tyagachyov had submitted a letter of resignation.
However, a spokesman for Mr Tyagachyov said the press attache of the Russian Olympic Committee "was hasty in dismissing his manager".
In his statement on Monday, Mr Medvedev had warned that if sports officials were reluctant to step down, "we will help them".
A former sports minister, Mr Tyagachyov , 63, had been appointed in 2001 and was seen as influential in helping Russia win the 2014 Winter Olympics.