An Indigenous man is reportedly fighting for life after falling to the tarmac during an airport transfer with the Royal Flying Doctor Service in WA's Pilbara region last week.

The man, understood to be in his 40s, is reportedly at Royal Perth Hospital after sustaining head injuries in the incident in the remote coastal town of Onslow.

He is said to be in a critical yet stable condition.

First reported by The West Australian, the man was on a trolley being wheeled to a plane at the time of the fall.

It occurred ahead of the long journey south to the state's capital, with the man already suffering serious health issues.

The fall is understood to have worsened his condition.

Family members have travelled to Perth to be with the man, who are reportedly upset and angry with what has occurred.

The RFDS has so far not provided details on the incident, but did say the matter is under investigation.

"Our thoughts are with the patient and his family at this very difficult time," RFDS chief executive Judith Barker said, via the West Australian.

"As this matter is currently under investigation, the Royal Flying Doctor Service is unable to provide any detail at this stage.

"The RFDS is working with St John WA to investigate this matter and ensure the family is supported. The safety and care of every RFDS patient is our highest priority."

Ambulance service St John WA reportedly also declined to comment on specifics of the incident.

WA Country Health Service is said to have originally requested the transfer, but the man was not in their care at the time of the incident.

"It is our expectation that the transport providers involved will complete a full and thorough investigation," a WA Country Health Service spokesperson told the West Australian.

"In the interim, we will continue to closely support the patient involved and their family. We know this is an extremely difficult time for them.