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.
The German Olympic Sports Confederation (DOSB) said on its website that Gauck had not been planning to visit to Sochi "according to our knowledge."
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."
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."
German Chancellor Angela Merkel spoke against boycotting the games in Sochi last August, in response to Russia's new law banning alleged gay propaganda. The chancellery said the games in February would focus attention on such issues, and that athletes would be most affected by a boycott.
Arrangements for Merkel's attendance at Sochi have not yet been made.