Gauck took the decision to protest human rights violations and the harassment of Russian opposition political figures, Der Spiegel reported today. The magazine said the Russian government was informed of his decision last week.
Presidential spokeswoman Ferdos Forudastan confirmed the move to the dpa news agency today. Gauck's office could not immediately be reached for further confirmation.
Forudastan told dpa that there was no set rule saying German presidents had to travel. Former president Horst Koehler did not travel to Vancouver for the Winter Games in 2010.
DOSB director general Michael Vesper told dpa that "(someone) who doesn't travel doesn't automatically boycott something. It's certainly not directed against the German team."
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Gauck, an outspoken critic of Russia's human-rights record, is yet to visit the country since taking office in March 2012. A planned meeting with Russian President Vladimir Putin in June 2012 fell through, apparently for scheduling reasons.
Gauck travelled to the Olympic Games and Paralympic Games in London last year.
Alexei Pushkov, the Kremlin-connected head of the Russian parliament's lower house, quickly responded to the perceived slight on Twitter: "Gauck never condemned the killing of children and women in Pakistan and Afghanistan. But he denounces Russia (so strongly) he would not go to Sochi."
Arrangements for Merkel's attendance at Sochi have not yet been made.