The plan to base the hub at the airport in Ulyanovsk, the birthplace of Russian revolutionary Vladimir Lenin, has drawn criticism from opponents, who say it would threaten Russia's national security, the RIA Novosti news agency reported.
The plan to use the base comes as NATO prepares to pull out of Afghanistan.
Russian Foreign Minister Sergei Lavrov told lawmakers last week, "We are helping the coalition ... primarily out of our own national interest." He called the plan "a means to assist those who are eradicating the threats of terrorism and drug trafficking in Afghanistan."
But the Communist Party called the plan a "threat" to Russia's "national security."
"The Communist Party decisively condemns the intention to ensure a permanent foreign military presence in the heart of Russia and demands that the Russian leadership stop the implementation of this idea," a party statement said.
"For the first time in the history of the Russian Empire, the U.S.S.R. and the Russian Federation, a foreign military base would appear on our soil … a base of a military bloc that the majority of our population view as hostile."
RIA Novosti said analysts dismissed concerns about the plan as a product of Cold War-era rhetoric and say the hub would benefit both Russia and NATO.