The panda's hormone levels combined with changes in her behavior suggest she may be expecting a cub, the result of an artificial insemination procedure carried out in April, they said.
A baby giant panda has never been born in Britain. Tian Tian and the zoo's male, Yang Guang, are the country's only pair of giant pandas but have twice tried and failed to mate naturally.
"Things are looking good," zoo spokesman Iain Valentine said, noting Tian Tian could have twins by different fathers, Yang Guang being one of them.
"We used two different males for the artificial insemination," he told BBC News.
Zoo officials caution it could be a pseudo -- or phantom -- pregnancy, extremely common in pandas.
But her behavior is an encouraging sign, they said.
Tian Tian's eating habits have changed, she is often moody and in the past few months has been showing "nesting" behavior, officials said.
If Tian Tian is indeed pregnant, zoo officials say the birth would likely occur from Aug. 24 and Sept. 10.
Since Tian Tian and Yang Guang are being rented by the zoo from the Chinese government for 10 years at an annual fee of nearly $1 million, any cub or cubs born would be the property of the People's Republic of China and would be sent there after two years in Scotland, they said.