Tian Tian and Yang Guang -- Sweet and Sunshine -- could be delivered to the zoo on Sunday.
It is thought the pandas will need time to settle into their new home before they go on display to the public. However, their arrival at the weekend would mean a pre-Christmas visitor boost for the zoo.
The pandas were given to the UK as a gift from China during a visit from the Chinese vice-premier Li Keqiang this year.
The duo are expected to arrive at their new home just days after First Minister Alex Salmond flies to China to boost links between the two countries.
An Edinburgh Zoo spokesman last night said: “We cannot confirm whether they will be arriving next week or not. Everything is prepared for their arrival and we are ready for them, so it will be a relatively short process.”
Originally it was hoped the pair, who will become the first such animals to live in Britain for 17 years and the first to live in captivity in Scotland, would be in their new home in time for the Duke of Edinburgh’s visit in August.
A series of delays led to the postponement of their arrival date. A Chinese delegation, sent to inspect the £250,000 panda enclosure, said improvements were needed before it would be suitable for its new occupants.
Alison Maclean, the keeper who will be in charge of the bears at Edinburgh, has recently returned from a three-week visit to the sanctuary to get to know the pandas and their routines.
Ms Maclean, team leader of giant pandas and carnivores at Edinburgh, said she had been left enchanted with the pair. They are so very different from any other animal,” she said. “They’re quite enchanting, not just in the way they look but the way they behave as well -- they’re different in the way they like to sit down and hold on to things, and the interest they take in what’s going on around them.”
Edinburgh Zoo -- which has been criticised by animal rights activists over the decision to move the pandas from China -- hopes the pair will breed.
Mr Salmond and Anne MacColl, chief executive of Scottish Development International, will travel to China for a series of high-level government, cultural, business and trade engagements in several mainland cities and Hong Kong.
Mr Salmond said: “China is the world’s fastest growing major economy and it is vital that government, business and other organisations enhance our already strong ties with this great nation.”