The arrangement, first reported by Foreign Policy magazine's online blog The Cable, follows publication of a Putin op-ed published in Thursday's New York Times.
The Russian leader warned in that piece that an attack on Syria over its alleged chemical weapons use "would increase violence and unleash a new wave of terrorism," and undermine efforts to resolve the Iranian nuclear problem.
"If John McCain wants to write something for us, he is welcome," Dmitry Sudakov, the English editor of Pravda, told Foreign Policy.
McCain's spokesman Brian Rogers told AFP that the veteran senator and 2008 Republican presidential nominee "is glad to take them up on the offer and will submit a piece."
More From This Section
Several US lawmakers expressed alarm at Putin's essay, including McCain who called it "an insult to the intelligence of every American."
In an interview with CNN, McCain noted Russia's poor press freedom record and quipped that "I would love to have a commentary in Pravda."
Pravda ("Truth" in Russian) was founded in 1912 by Bolshevik revolutionaries and served as the mouthpiece for the Kremlin until the 1991 break-up of the Soviet Union.
An organ of the Communist Party, it is no longer considered one of the country's main newspapers.