According to reports, the group has appointed headhunters to help its search for a new boss.
Cescau, who is nearly 60 and has spent 35 years at Unilever, is preparing to step down next year at a time of his own choosing. Reports suggest that he is likely to step down at Unilever's AGM next May.
Unilever is most likely to replace Cescau with an internal candidate. Those in the running include: chief financial officer Jim Lawrence; Americas division president Mike Polk; foods, home and personal care president Vindi Banga; and Asia president Harish Manwani.
During his tenure at Unilever, Cescau more recently conducted a strategic overhaul of the group's brands under the banner "One Unilever". Last week, the group also arranged the £500m sale of Bertolli, its olive oil brand, to Spanish food producer Grupo SOS.