Listyev was a prominent Russian journalist and television presenter. He was shot dead on March 1, 1995 in the building where he lived.
The Russian producers of the film, which is planned to be released on the anniversary of Listyev's death in 2017, see Stone as one of the candidates for the director's post, according to the press release.
"We hope that the participation in a project of such significance for Russia as a film about Vladislav Listyev will be a natural way for Oliver Stone to continue strengthening his cinematic ties with Russia," Oleg Teterin, one of the producers of the film, was quoted as saying in the press release.
A competition to write a script for the film is currently open. Entrants are free to base their screenplay on either the journalist's biography, which covered his life between 1987 and 1995, the murder investigation, or the last 24 hours of the journalist's life.
"The film will be dedicated to the memory of killed Russian journalists, politicians and public figures," Alexander Kulikov, another producer of the project, was quoted as saying in the press release.
On April 21, 2009, the investigation into Listyev's death was suspended, with those behind the murder still not found.
Three-time Oscar winner Stone is currently involved in a project about former US National Security Agency (NSA) contractor Edward Snowden, based on the book by the whistleblower's Russian lawyer, Anatoly Kucherena. The film is due to hit theaters in 2015.
