Chef de Mission Mike Hay said he will be taking advice from people on the ground in order to protect his stars before February's event.
The event is dogged by two controversies, firstly the passing of draconian anti-gay laws and secondly, growing fears of attacks by the Caucasus Emirate and Russian Islamist terror group.
Mr Hay's comments during an event at the Braehead Arena near Glasgow came as the all-Scottish world champion women's curling rink of Eve Muirhead, Claire Hamilton, Vicki Adams and Anna Sloan were named as the first members of the squad.
He said: "I heard something this morning about the Caucasus mountains that somebody had been killed and you hear a lot of these stories, and a lot of it just happens all the time in these places so I don't think we should be unduly worried.
"But at the same time we'll be taking advice from the people who are there and they'll let us know if there is a direct threat to Team GB athletes. We are concerned, of course we are, but ultimately there are a lot of mixed messages coming out of Russia at the moment."
He added that Team GB was working closely with the Foreign Office and the International Olympic Committee in an attempt to understand the situation better.
He added that while the principal responsibility for protecting those attending the Games lies with the Russians the British Olympic Association is taking all the precautions it can to safeguard athletes.