A source close to the matter said the case involved meldonium, which is the same substance that saw Maria Sharapova banned.
The World Curling Federation also said it was aware of the situation, following Russian reports which named a Russian curler.
Russia was banned from the Olympics after the emergence of "systemic" doping. But the International Olympic Committee is considering lifting the ban before the Pyeongchang closing ceremony on 26 February.
A fresh doping case would be deeply embarrassing for Russia, which has 168 athletes deemed clean competing in Pyeongchang as neutral Olympic Athletes from Russia.
"Today the headquarters of our delegation received an official notice from the IOC regarding a possible violation of anti-doping rules," Konstantin Vybornov, spokesman for the Russian team, was quoted as saying earlier on Sunday.
"We are not naming the athlete or the discipline until the B-sample results, which are expected within approximately 24 hours," he said, according to Russian media.
If the case is confirmed, it will come before the Court of Arbitration for Sport, which is handling doping matters at the Olympics and has an ad hoc division in Pyeongchang.
It would also be considered by the panel which will ponder whether to end Russia's ban as early as next week, the IOC said.
"On the one hand, it is extremely disappointing when prohibited substances might have been used but, on the other hand, it shows the effectiveness of the anti-doping system at the Games, which protects the rights of all clean athletes," an IOC statement said.