The rumor surfaced on October 11, when senior Moscow Duma deputy Andrei Metelsky said the monument may be brought back to its "rightful" place on Lubyanka Square -- once home to the headquarters of the KGB, the Cheka's Soviet-era successor.
He was speaking a day after a city committee announced that Moscow was refurbishing seven monuments, including the one of Dzerzhinsky, for a total of over 50 million rubles ($1.5 million) in public money.
Metelsky, a member of the ruling United Russia party, described the statue as a historical landmark and said that since Moscow authorities had allocated the money to bring it back to life, "then the process must be completed."
His statement was quick to make headlines, eventually prompting Metelsky to clarify that he had only been stating his personal opinion. He accused journalists of misinterpreting his words.
City council speaker Vladimir Platonov later stepped in to quash the budding controversy, stressing that parliament had no say in choosing the monuments that grace the capital.
Dzerzhinsky's statue has raised passions since the fall of the Soviet Union.
The Cheka, founded in 1917 by Dzerzhinsky, nicknamed "Iron Feliks," is known for having overseen a ruthless campaign of torture and repression that killed hundreds of thousands of people in the six years that followed the 1917 Bolshevik Revolution.
The bloodshed set the tone for the brutal repression carried out by Soviet dictator Josef Stalin in the 1930s.
After the failed coup by Politburo hard-liners against Soviet President Mikhail Gorbachev in August 1991, the Dzerzhinsky monument on Lubyanka Square was toppled by a crowd of protesters, who used a crane to dismantle it in a now-iconic episode of the months leading up to the Soviet collapse.
There have since been numerous calls to return the statue, testifying to the ambivalent feelings of Russians about their past.
President Vladimir Putin himself has abundantly tapped into Soviet nostalgia, restoring the red star as the symbol of the military and bringing back the music of the old Soviet anthem.
In 2005, a bust of Dzerzhinsky was placed in the courtyard of the Russian Interior Ministry headquarters, sparking some criticism.
But Putin has stopped short of returning the full-sized statue, which has been lingering with other discarded Soviet statues in Moscow's Fallen Monument Park, to its original location.
Veteran human rights campaigner Lyudmila Alekseyeva says this is unlikely ever to happen.
"Rumors that this monument will be restored emerge from time to time, but I don't believe it's possible," Alekseyeva says. "This monument symbolizes a grim institution that [created] millions of innocent victims. I think any attempt to restore this monument will generate loud protests and is unlikely to succeed."
Moscow's former mayor, Yury Luzhkov, has been one of those championing the statue's return.
But he, too, has encountered opposition from liberals, rights advocates, and the Russian Orthodox Church, whose priests were persecuted by the Cheka.
Critics point out that Lubyanka Square is already home to the Solovetsky Stone, a monument to commemorate the victims of Soviet political repression that was installed less than a year before Dzerzhinsky's statue came down.