Two fire appliances were sent to the scene in the iconic glen, however, they were stood down shortly after arriving.
The service said the decision was taken to leave the fire to burn itself out as there was no threat to people or property.
A statement from the police said: “Police in Glencoe are appealing for information regarding a hill fire set on the slopes of Ben Starav at the foot of Glen Etive on Friday 30 April 2021 around 3:50pm.
“Enquiries are ongoing to establish whether this was a deliberate act or not and anyone with any relevent information is asked to contact Police on 101 or crime stoppers on 0800 555 111 if you wish to remain anonymous.”
A spokeswoman for the fire service said on Saturday: “We received a call at around 3.58pm yesterday evening.
“We mobilised two fire appliances to the fire in the open. We received the stop message back at around 5.26pm.
“Due to there being no risk to property, the fire continued to burn well up on the hill.”
Police appeal for witnesses after hill fire in Glen Etive