According to L’Equipe, Cahuzac's departure has yet to be officially confirmed, although the Frenchman has already returned to his native Corsica.
His anticipated exit follows a turbulent nine-match spell, culminating in three consecutive defeats against Lille, Como and Marseille.
The humiliating 9-1 Champions League loss to Como, which equalled the competition's heaviest defeat, further intensified pressure on the manager.
Lens president Joseph Oughourlian reportedly favours appointing Pierre Sage, whose future at Crystal Palace remains uncertain.
Former Le Havre coach Didier Digard is another candidate under consideration alongside Beye.
Beye previously managed Rennes and Red Star, gaining valuable experience in French football before his Marseille appointment.