Dr Ken Elliot and his wife Jocelyn Elliott are believed to have been abducted in the north of Burkina Faso following a deadly attack on the capital last week.
The couple, in their 80s moved to Burkina Faso in 1972 and established a medical clinic in the northern town of Djibo.
Ken and Jocelyn Elliot were abducted by suspected Islamist extremists, following an attack on the capital of Ouagadougou on Friday that killed at least 29 people from 18 countries.
Dr Elliot performed 150 surgical operations a month in the Friends of Burkina Faso Medical Clinic, which he designed and built himself.
Dicko Seydou, is a friend of the Elliots' and is behind a social media campaign calling for their release.
"Make a kind of advocacy plan to make people aware of what is happening now and help us to find ways to release these doctor. For us, he's not only Australian but he's someone from Burkina Faso, someone from our community, what he did for our community even the government itself couldn't do more than that and since really so long time."
An Australian who was held hostage in Somalia for 15 months and only freed after his family paid a ransom says his thoughts are with the couple.
Photojournalist Nigel Brennan believed it was unlikely the couple's Christian faith would adversely affect their situation, saying the hostage-takers may see their belief in God as a "good thing".
Mr Brennan, who was critical of the then-Rudd government's handling of his own situation, hoped the Turnbull government was talking to the kidnappers about options for release.
But he noted it was illegal for the government to pay any ransom.
Mr Brennan says the couple are likely to be feeling a sense of shock over their kidnapping.
"Within the first few hours we realised that we had been kidnapped but there is also still that shock of is this happening is this a dream. Am I going to wake up. Hopefully I am going to wake up from this dream and I guess that sort of moved into for me anger, also for me it was a lot of guilt and shame for what I was putting my family through."
While the whereabouts of the Elliots is unknown there are unverified reports they may have been smuggled into neighbouring Mali following the attack on Ouagadougou.
Burkina Faso and Mali have agreed to work together to counter the growing threat of Islamic militants in West Africa by sharing intelligence and conducting joint security patrols following two deadly attacks in the region.
Burkina Faso Prime Minister Paul Kaba Thieba says both countries will step up efforts to counter the threats they're facing.
"There is a very strong political will on the part of the two states to combine our efforts to fight a terrorism that has now become a transnational phenomenon affecting all of our countries, and the head of state has agreed to intensify cooperation with Mali in affairs of information sharing, joint patrols, and many other fields."
