According to Moroccan daily, Assabah, the Security Council may also give Morocco a green light for limited military intervention against the Polisario Front who they accuse of attempting to relocate parts of its facilities to Morocco's eastern defence wall.
Le Drian's statement comes following an official meeting between King Mohammed VI and French President Emmanuel Macron this week at the Elysee Palace.
"If the Polisario does not withdraw from the buffer zone, as provided by the ceasefire agreement, Morocco has the right to respond with firmness," Le Drian told Algerian foreign minister AbdelKader Messahel.
Messahel reportedly held a meeting with the staff from Algeria's National People's Army to inform them of France's position and its support for Morocco's military intervention.
The Western Sahara is a disputed territory between Morocco, which views it as a part of its sovereign Kingdom, and the Polisario, which represents the indigenous Sahrawi people and which has been fighting for the self-determination of the Sahrawi people for the last 27 years.
Speaking in an interview with France 24, Messahel reiterated how the Western Sahara conflict is one that should be solved between Morocco and the Polisario and that Algeria should not be pressured in to finding a solution.
His comments were in response to a letter addressed to the UN Secretary-General Antonio Guterres calling on Algeria to shoulder its responsibility in finding a solution to the regional conflict.
According to Messahel, Morocco claims that the Western Sahara conflict is "a matter between Algeria and Morocco", but "it is not the case".
"It is a case between Morocco and the Sahrawi people, and between Morocco and the decisions of the United Nations."