Amunai Hobbs, 41, also known as Amunai Nicholson, from Oban, left the airport on Thursday saying she felt unwell.
There have been no confirmed sightings since she left Royal Alexandra Hospital in Paisley without treatment at 10:35.
However, one report has placed her about halfway between the hospital and the airport a short time later.
The witness said she may have been on Inchinnan Road, near Fleming Street, between 11:30 and 12:30 and did not appear to be wearing shoes.
Police have renewed their appeal for sightings of Ms Hobbs, who is from Thailand but lives in Scotland.
She is described as about 4ft 10 in tall, of slim build with short black hair.
At the last confirmed sighting she was wearing a beige-coloured fur coat, a purple dress with staining down the front, purple leggings and brown boots.
The reported sighting on Inchinnan Road described a woman wearing a grey cardigan with large buttons on the front, black cropped leggings and she was not wearing shoes.
Insp Gary Noonan said: "Searches are continuing using a number of resources including the force helicopter and specialist search officers, however we have yet to trace Amunai.
"This is a very distressing time for her family and friends and they are extremely concerned for her wellbeing and safety. It is out of character for her not to keep in contact with them.
"I would urge anyone with any information on her whereabouts, or has seen someone matching her description to contact Paisley Police Office on 101."
A woman who disappeared after missing her flight to Thailand may have been sighted walking without shoes in the street near Glasgow Airport.