The Duval family has written a letter suggesting the metals and mining firm replace chairwoman and CEO Christel Bories, business newspaper L'Agefi reported.
The Russian miner said profit attributable to shareholders totalled $2.25 billion (131.39bn roubles) last year, versus $530K (30.67bn) roubles in 2015.
The company is currently analyzing options to resume work as soon as possible, which includes hiring temporary workers to replace those that have downed tools.
The company expects demand to increase 3% this year, while no new mines are scheduled to come online in the short-term and supply disruptions continue.