“What the hell is going on - these are extremely lovely people. I really hope they are fine and well,"another wrote.
The couple's last post was from western Kyrgyzstan in late June.
"We definitely don't have anything to complain about,"a comment from the couple's Facebook account read.
Their Instagram geolocation says that the pair are"Currently:Taking a Break."
Images from their website and social media presence over the past two years shows a number of images of the pair and their Toyota troop carrier taken by drone. But DFAT's Smart Traveller advice suggests photography in Iran,particularly around military installations,could be problematic in a nation with a risk of"arbitrary detention".
"It would be highly unlikely that the Government of Iran would allow the Australian Government to provide consular assistance to you if you are arrested or detained,"the website reads.
"You may be at greater risk if you have a profile ... or if you undertake certain activities which could attract the attention of Iranian authorities. These may include travel off the beaten track,being present near sensitive sites[or] taking photographs."
Australian Michele Rankin met the"wonderful couple"in East Timor and spoke of their generosity.
"They spent a few days helping us to deliver much needed supplies to schools in remote areas ... thinking of you,"she wrote on Facebook.
London'sThe Times has reported Ms King is believed to be imprisoned as a bargaining chip for a prisoner swap with Iranian womanNegar Ghodskani,who was extradited from Australia to the USand charged with a conspiracy to export prohibited technology to Iran.
Ms Ghodskani,40,was arrested in Australia at the request of US authorities and gave birth in prison in Adelaide.
She has pleaded guilty to the charge,which carries a sentence of up to five years in a federal US prison.
"Let’s have an exchange. I’m ready to do it. I have the authority to do it,"said the Islamic Republic's Foreign Affairs Minister Mohammad Javad Zafir in April.
Iran has yet to comment on the arrests or diplomatic attempts being made by Australia.
The arrests come weeks after Prime Minister Scott Morrison agreed to a US-led military effort to protect ships passing through the Strait of Hormuz,which is to the south-west of Iran.
About one-fifth of the world's oil passes through the Strait sees and Western nations are concerned about what Mr Morrison called"destabilising behaviour"affecting Australia's interests.