A DWFRS spokesperson said: "The cliff does not spontaneously combust, despite the warm weather we've been experiencing, so we do believe there to have been some human intervention.
"However, we cannot determine whether that is accidental or deliberate."
The fire service said the blaze was extinguished by 23:00 but crews returned to the scene at 06:00 to check for hot spots which could flare up.
In an update at 13:00, the fire service explained the incident "would remain open for a reinspection again this afternoon".
It added crews had found several hotspots and the cause of the fire would be "difficult to determine due to the nature of the incident".
DWFRS said it received more than 60 calls about the blaze near Bournemouth pier on Saturday.
Crews from Springbourne, Westbourne, Poole, Ferndown, Christchurch and Wimborne tackled the flames, which covered an area about 328ft (100m) square.
Bournemouth, Christchurch and Poole (BCP) Council said in a statement the cause of the fire "is unclear" and listed advice from the fire service to avoid wildfires.
The guidance includes not having fires or barbecues near heathlands or clifftops, extinguishing smoking materials properly and not throwing cigarette ends on the ground or out of car windows.
The fire took place about 164ft (50m) away from the goats' enclosure, said a council spokesperson, adding: "All the goats are safe and well."
