PYEONGCHANG, South Korea — With Russia performing feebly at the Winter Games because many of its best athletes are barred for doping violations, the Russian oligarch who owns the N.B.A.’s Brooklyn Nets is helping to finance an attempt to attack the credibility of the whistle-blower who exposed the country’s elaborate doping program.

The oligarch, Mikhail D. Prokhorov, who led Russia’s biathlon federation before and during the 2014 Sochi Games, is backing a long-shot legal effort against the whistle-blower, Dr. Grigory Rodchenkov, that will commence with a defamation lawsuit to be filed in New York State Court on Tuesday.

The suit, which The New York Times reviewed before it was filed, claims Dr. Rodchenkov defamed three now-retired Russian biathletes — Olga Zaytseva, Yana Romanova and Olga Vilukhina — when he linked them to the state-controlled scheme that corrupted the last Winter Games in Sochi, Russia.

The women, who were stripped of the silver medal they secured in a relay event at the Sochi Games, are seeking $10 million each in damages.