The newspaper said that under the plan, only aircraft deployed to protect energy facilities, and planes of top Russian officials or of visiting foreign officials would be allowed to fly with special permission in the designated zones.
Russia's energy ministry did not immediately comment on the report.
Russian air defences thwarted a drone attack on Monday on the Slavneft-YANOS oil refinery in the city of Yaroslavl, northeast of Moscow, regional governor Mikhail Yevrayev said.
It was the latest in a series of similar drone raids on Russian energy infrastructure in recent weeks, some of which have disrupted fuel production.
Ukrainian officials have said Kyiv is behind some of the attacks.
Russia's nearly two-year-old war in Ukraine is grinding into a war of attrition following delays in Western financial and military assistance for Kyiv, and without significant changes on the battlefield in months.
Russian energy company Novatek NVTK.MM suspended some operations at a huge Baltic Sea fuel export terminal on Jan. 21 after a fire started by what Ukrainian media said was a drone attack.
Two days before that, a drone attack had hit an oil depot in Russia's western region of Bryansk, bordering Ukraine, for which Moscow blamed Kyiv. That followed an attack a day earlier on a Russian Baltic Sea oil terminal that Russian officials said was unsuccessful.
(Writing by John Davison in Geneva, Editing by Timothy Heritage)
