Its investigation - described as "highly credible" by veteran Nazi-hunter Serge Klarsfeld - aims at resolving the fate of one of the most notorious figures of the Holocaust.
Three ex-members of the Syrian secret service interviewed by the magazine XXI said Adolf Eichmann's former assistant spent his last years in miserable conditions underneath an apartment block in the Syrian capital.
The Austrian-born SS commander was in charge of the Drancy camp north of Paris from which Jews in occupied France were sent to the gas chambers.
He remained to the end an unrepentant Nazi and anti-Semite, the sources told XXI.
One of his guards said Brunner, who went by the name of Abu Hussein, "suffered and cried a lot in his final years, everyone heard him".
The man, identified only as Omar, said he "couldn't even wash".
All he had to eat were "army rations - awful stuff - and an egg or a potato. He had to choose one or the other."
The circumstances of Brunner's final years have remained an enigma for decades.
The Simon Wiesenthal Centre in Vienna, which tracks down former Nazis, had declared that he had died in Damascus in 2010.
Klarsfeld, a prominent lawyer and historian, flew to Syria with his wife and fellow investigator Beate in 1982 to urge the Assad regime to expel him.
Klarsfeld's father was arrested in Nice in September 1943 in an SS roundup led by Brunner. He later died in Auschwitz.
Eichmann's 'right-hand man'
Eichmann, one of the architects of the so-called Final Solution who was hanged in Israel in 1962, called Brunner his "right-hand man".
"We are satisfied to learn that he lived badly rather than well," Klarsfeld told AFP.
"XXI's investigation is highly credible. They have questioned someone who knew him at close quarters," he added.
Brunner slipped through the Allies' hands at the end of the war.
He left Germany for Egypt in 1953 with a passport in the name of Georg Fischer.
He worked for a time running guns to the Algerian independence movement, the FLN, before moving to Syria the following year.
Sheltered in Damascus, he became an advisor to the Syria secret police, allegedly passing on torture and interrogation methods developed by the Nazis.
Survived parcel bombs
But the Israeli intelligence services were quickly on his trail.
He was said to have been killed by a parcel bomb on September 13th, 1961.
In fact, he lost an eye in that attack and four fingers in another parcel bomb in 1981, although the Syrian authorities continued to deny his existence.
He was convicted of war crimes by French courts in his absence in 1954, when he was sentenced to death.
In 2001, another French trial, which for the first time included the specific charge of arresting and deporting hundreds of orphans, sentenced him to life imprisonment. The death sentence had been abolished in France in 1981.
According to XXI, Brunner was practically under house arrest in his apartment in the diplomatic quarter of Damascus from 1989.
It said at the end of the 1990s he was moved for "security reasons" to the basement, and he was confined there until his death.
"Once he was in the room, the door was closed and never opened again," Omar told the magazine.
He claimed Brunner was buried secretly in accordance with Muslim rites in the city's Al-Affif cemetery in December 2001.
"In a dictatorship like Syria, he was untouchable as long as the dictator didn't want rid of him," said Klarsfeld.
"Until the end he kept his hatred of Jews intact, as well as his faith in National Socialism," he added. "He was someone who hated France as much as he hated Jews."
In a short telephone interview in 1987 Brunner is alleged to have told the Chicago Sun-Times that he didn't regret his part in the Holocaust.
"All of them deserved to die because they were the devil's agents and human garbage. I have no regrets and I would do it again."
By Alain Jean-Robert and Fiachra Gibbons, AFP