The organization's joint command and some 41,000 military personnel are to be summoned to practice repelling a Russian attack against a member of the alliance, as the newspaper wrote.
The exercises dubbed "Steadfast Defender" are to be held next spring.
Sweden, whose full accession to NATO is yet to be approved by Hungary and Turkey, is expected to join the military drills.
Last September, Russian President Vladimir Putin addressed citizens, saying that the West had overstepped all limits in its anti-Russian politics and threats. Putin said that Russia's production is superior to foreign military hardware in a number of components and warned those trying to blackmail Moscow with nuclear weapons, adding that "the wind may turn in their direction."