Russian media reported on Wednesday that the court ruled that the Arbitration Court in the field of sport (CAS) should not apply to Russian territory.
However, the court decision has no effect outside the country, with the result of 2014 remaining unchanged, and the DAC's decision is intact.
The International Olympic Committee (IOC) took Zubkov's life out of two bobsleigh gold medals last year and banned him at the Olympics for life because of drug addictions that Zubunkov denied.
He appealed to CAS, but the court upheld the IOC's decision.
Zubkov, who withdrew from the competition and is currently the president of the Russian Federation, told TASS: "My status as Olympic champion on the territory of the Russian Federation is important to me."
Russian athletes were banned from the IOC to compete officially at this year's Winter Olympics in Pyeongjiang for the "systemic manipulation" of Sochi's doping tests in 2014.
The IOC allowed Russians who do not have a history of doping to compete on the invitation of the Games as neutral athletes.
Russia has categorically denied that the country is sponsored by the state.