Khadzhikurbanov was one of five people jailed in 2014 over Politkovskaya's murder, but investigators at the time did not identify the person who ordered the killing.
In 2018, the European Court of Human Rights determined that although authorities had convicted the group of men directly involved in the killing, they had "failed to take adequate investigatory steps to find the person or persons who had commissioned the murder."
Russia's Washington embassy did not immediately reply to VOA's email requesting comment.
Politkovskaya, who was 48 years old when she was killed, is among at least six Novaya Gazeta reporters and contributors who have been killed since 2000.
In the fall 2006 edition of the CPJ's magazine Dangerous Assignments, the press freedom group named Politkovskaya as one of the world's top press freedom figures of the past 25 years.
In an email interview with CPJ shortly before her killing, Politkovskaya said she was frustrated with the declining press freedom situation in Chechnya. She cited the deadly 2004 hostage crisis in the North Ossetian town of Beslan as an example.
"There is so much more to write about Beslan," she told CPJ, "but it gets more and more difficult when all the journalists who write are forced to leave."