Abdeslam, 26, exercised his right to remain silent on Thursday morning, the third time he has refused to answer anti-terror judges' questions since he was transferred to France from Belgium in April.
He is believed to be angry at round-the-clock surveillance in jail.
On July 7th his lawyer Frank Berton sought unsuccessfully to get authorities to halt the surveillance, the source said.
Abdeslam is a member of the jihadist cell which killed 130 people in a series of attacks in Paris in November, although investigators are unsure as to his exact role.
Authorities hope Abdeslam will be able to shed light on the operational details of the Paris attacks, as well as provide clues as to whether other cell members are still at large.
For months, Abdeslam was the most wanted fugitive in Europe until he was tracked down and arrested on March 18th in the Brussels neighbourhood of Molenbeek where he grew up. Transferred to France under high security on April 27th, he has since been held at Fleury-Merogis prison, southeast of Paris.