The animal is a deep-diving species thought to have drifted in from its feeding grounds about 50 miles west of the islands.
Wildlife photographer and writer Hugh Harrop said the whale had semi-stranded at least twice in 10m (33ft) deep water around South Whiteness.
He said it was hoped the animal would find its way back to open sea.
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Mr Harrop told BBC radio's Good Morning Scotland programme the whale was being monitored from a distance with the use of a drone.
On Wednesday the coastguard tasked a team to observe the whale after reports that a small boat had got close to it as bystanders watched from the shore.
Sperm whales have previously got into difficulty on Scotland's coast.
A 66ft whale died in January 2020 after getting into difficulty at Ardersier near Inverness.
In 2019, a sperm whale died after stranding on the Isle of Harris.
It was later found to have had a 100kg "litter ball" in its stomach.
Fishing nets, rope, packing straps, bags and plastic cups were among the items discovered in a compacted mass discovered during a necropsy on its remains..
In August 2008, a 40ft adult sperm whale died after stranding in shallow water in the Moray Firth at Arturlie Point close to Inverness.
The skull of a 40ft sperm whale found beached on the banks of the River Forth at Airth in Stirlingshire in March 1997 is now on display at the National Museum of Scotland.
The whale, known affectionately as ‘Moby’, was the first sperm whale to be stranded in the Forth in over 200 years. He beached despite a massive operation to turn him downriver involving volunteers, marine mammal experts and the emergency services.
Following his death, Moby’s skeleton was prepared by museum staff and is now in National Museums Scotland’s Natural Science collections, which is home to several million specimens, including one of the largest marine mammal collections in the world.
Moby tasted fame again in 2009, when his skull was loaned to Glasgow-based Turner Prize nominee Lucy Skaer for her work ‘Leviathan Edge 2009’ at Tate Britain.