Police discovered two cylinders of gas in the hall of a building in the city's posh 16th arrondissement on the western edge of the capital and two others on the pavement.
They also found a mobile phone linked to the cylinders, which appeared to be “a device to ignite” the explosive, the sources said.
A resident alerted police after finding two of the gas cylinders around 4:30 am (0230 GMT) on Saturday in his building in the Porte d'Auteuil neighbourhood, a source close to the probe said.
Police then found the other two cylinders outside the building, believed to be on the quiet Rue Chanez, which runs parallel to Boulevard Exelmans and is a short walk from the Parc des Princes, where Paris football team PSG play their home matches.
Reports said the improvised device had been soaked in petrol and was “operational”.
(Google street view)
According to another AFP source, five suspects were being held in custody Monday night. According to Le Point magazine the main suspect has links to the radical Islamist movement and was known to intelligence services.
It remains a mystery why the bomb was left outside the building on what is a quiet street in one of the French capital's plushest neighbourhoods.
According to French media, police have said there was no one living in the apartment block who might be considered a target for jihadists.
(The bomb was left outside this building on Rue Chanez. AFP)
But one theory put forward by Le Figaro newspaper is that the bomb makers may have wanted to target an association that battles radical Islam but got the wrong address. This has not been confirmed by any official figure.
France's Interior Minister Gerard Collomb suggested the motivation may simply have been to create fear.
“Blowing up a building in a chic neighbourhood shows that no one is safe… it shows that it could happen anywhere in France,” the minister told France Inter.
The terrorist threat remains high in France, which has been hit with a series of jihadist attacks since January 2015.
The latest attack was on Sunday in Marseille when a knifeman stabbed two women to death at the main train station shouting “Allahu Akbar” (“God is greatest”). He was shot and killed by soldiers.
The stabbings bring to 241 the number of people killed in jihadist attacks in France.
On September 12, French Interior Minister Gerard Collomb said that 12 planned attacks had been foiled since the beginning of the year.