As it is very difficult to even tell if a panda is pregnant, keepers can only watch and wait - but the latest hormone tests continue to suggest that Tian Tian could give birth soon.
Zoo staff are hopeful that they will be welcoming a new arrival or two within the next two weeks.
"What we are seeing in Tian Tian's hormones is encouraging, but we still cannot guarantee a pregnancy or successful birth," Iain Valentine, Director of Giant Pandas for the Royal Zoological Society of Scotland, said.
"If indeed she is pregnant, this is an extremely risky time for panda pregnancies. Female giant pandas can actually reabsorb any foetuses or reject them if pregnant.
"If she is pregnant and carries to full term, we believe a cub or cubs could be born anytime over the next two weeks."
It will be incredible. It won't just be the first pandas born in Edinburgh Zoo, it will be the first pandas born in the country.
Tony Bradford, visitor experience coordinator at Edinburgh Zoo
Pandas tend to either have one cub or twins, but will reject one of a pair of cubs as they can only rear one at a time. If that happens at Edinburgh Zoo, keepers will hand-rear the rejected cub.
A Chinese panda-keeping expert, Haiping Hu from the China Conservation and Research Centre, has arrived in Edinburgh over the weekend and will be on hand to assist if necessary.
Tian Tian is said to be quite sleepy and has been spending increasing periods of time away from the public eye but, according to the zoo, visitors have been very understanding.
"Tian Tian's current routine is to spend a lot of her day sleeping in the cubbing box in her off-show indoor enclosure, though she does tend to come outside for a stroll and stretch on her climbing frame in the afternoons," Mr Valentine said.
"We are keeping the lights switched off for most of the day inside to help mimic the atmosphere of a den that she would seek in the wild."
Tian Tian and male giant panda Yang Guang arrived at Edinburgh Zoo amid worldwide interest in December 2011 after a 5,000-mile flight from China.
They are the first giant pandas to live in the UK in 17 years and will stay until at least 2021, with finance experts predicting that their 10-year stay will generate almost £28m for the Edinburgh economy and a further £19m for the wider Scottish economy.
However, all pandas - regardless of where they are born - are the property of the People's Republic of China.
If Tian Tian does give birth to a cub, in line with Chinese tradition, it would not be named until it is 100 days old and would only go on display from 1 January 2014.
When it reaches the age of two - the age pandas disperse in the wild, it would be taken to China and join the conservation programmes there to get pandas back into the wild.
Keepers are now able to access CCTV footage of Tian Tian from their homes so they can keep an eye on her at all times. Giant pandas start to show sign of labour 24 hours before the process begins.
About 24 hours before she gives birth, she will become quite restless, start moving around, and then will sit down - her waters will break and then, quite soon after that, she will give birth.
Iain Valentine, Royal Zoological Society of Scotland
Mr Valentine explained: "The birth process can be over quite quickly because the cub itself is very small. It could take minutes.
"It is down to the timing and her being comfortable. The cub is only 100 grams, so she doesn't have to strain too much to give birth."
In the wild, male giant pandas have nothing to do with rearing cubs, so Yang Guang won't have any contact with Tian Tian or any babies.
Any cubs born to Tian Tian at Edinburgh Zoo would be the first to be born in the UK.