The International Olympic Committee (IOC) on Tuesday banned Russia from the Pyeongchang Games after evidence emerged of an "unprecedented systematic manipulation" of the anti-doping system, but left the door open for clean athletes to compete as neutrals.
"We need to hold alternative competitions for the athletes who decide not to go to the Olympic Games," R-Sport quoted Zhukov as saying. "But we also need to support those who decide to go."
Zhukov, who did not provide further detail about the possible nature of those competitions, added that it was "unacceptable" to accuse Russian athletes who decide to compete at the Olympics of being unpatriotic.
President Vladimir Putin said this week that Russia would not prevent athletes from competing at the Games if they wanted to, damping down calls by some Russians for the country to boycott.
Russia is expected to make a final decision on its stance regarding the IOC ban at a meeting of the country's Olympic authorities next week.
Russian authorities have vehemently denied any state support for doping and have pledged to co-operate with international sports bodies to counter the use of banned performance-enhancing drugs.
The speaker of the Russian parliament, Vyacheslav Volodin, told lawmakers earlier on Friday that they should not attend the Pyeongchang Games if Russian athletes are not competing under the country's flag, local news agencies reported.
In the weeks ahead of Tuesday's IOC decision, more than 20 Russian athletes who competed at the 2014 Sochi Games were banned for life from the Olympics for having allegedly violated anti-doping rules.
Russia's athletics federation, Paralympic Committee and anti-doping agency RUSADA remain suspended over doping scandals.
(Writing by Gabrielle Tétrault-Farber,; Editing by Denis Pinchuk and Ed Osmond)
