The reports, which have not been officially confirmed, say that a discarded suicide vest was found in a bin in the suburb of Montrouge, just to the south of Paris.
After the discovery was made a security cordon was installed while forensics teams moved in.
BFM TV have quoted a source close to the investigation who said the bomb vest was similar to those used in the Paris attacks of November 13th.
If it is confirmed the object is indeed a suicide vest then it is highly likely it was linked to the attacks, which saw suicide bombers attack the Stade de France and the Bataclan, as well as a bar on Avenue Voltaire.
Reports also say investigators have have studied telephone data which places the wanted man Salah Abdeslam in Montrouge after the attacks.
Abdeslam was initially implicated in the terrace shootings, but there is a growing suspicion that Abdeslam was supposed to have launched an attack in the 18th arrondissement of the city and pulled out at the last minute.
He is the subject of a European-wide manhunt and is believed to be hiding out in Brussels, which is part of the reason why the Belgian capital remains in lockdown and on the highest level of terror alert.
Abdeslam was spirited away from Paris to Belgium after the November 13 massacre by two other men who were later arrested and charged there.
Like his brother Brahim, who blew himself up in a bar the night of the attacks, Salah played a key logistical role in the wave of terror that left 130 people dead.
The Obs news website reports that the two men held in Belgium told investigators that they found him in a state of shock and wearing an explosives vest when they came to spirit him out.
His brother Mohamed Abdeslam on Sunday told RTBF television he thought Salah decided at the very last moment not to go through with his attack.
Salah and his brother Brahim have been described as "big drinkers and big smokers" by friends who knew them from a bar they ran in Brussels that was shut down by authorities a few weeks ago.
The brothers grew up in the Brussels area of Molenbeek, a hotbed of Islamist extremism in Europe.
Both had links to Abaaoud, the alleged ringleader of the attacks, who also lived in Molenbeek.
On Monday Belgian authorities charged a fourth man in relation to the Paris attacks.