Experts at Edinburgh Zoo have been monitoring her since she was artificially inseminated on April 13 and last week it was revealed that "the latest scientific data" suggest she is pregnant.
The panda was successfully inseminated last year but lost her cub at late term, something the zoo is wary of again.
Tian Tian's hormone and protein levels are being checked regularly but it will not be known for certain if she is pregnant until she gives birth.
A spokeswoman for the zoo said today that things are progressing as expected and that they are "keeping their fingers crossed" for the arrival of a third panda.
Tian Tian, which means Sweetie, and male Yang Guang (Sunshine) arrived on loan from China in December 2011 and are the first giant pandas to live in the UK for 17 years.
The animals, now both aged 10, will remain at Edinburgh Zoo for a decade.
Speaking last week, Iain Valentine, director of pandas at the zoo, said: ''Monitoring a female giant panda's behaviour - for example, if she is sleeping a lot, eating more or spending time in her cubbing den - is not an indicator of if she is pregnant or otherwise, as giant pandas experience pseudo-pregnancies and she will show pregnant-type behaviour whether she is pregnant or not."
The zoo is being supported in monitoring the pregnancy by experts in Scotland and China.
The Royal Zoological Society of Scotland, which runs the zoo, and the University of Edinburgh have signed a new five-year "memorandum of understanding" to encourage further collaboration between the institutions.
Working together they were able to confirm key timelines in the female giant panda's breeding window and pregnancy by studying protein levels and hormone crossovers.
Endocrinologists at the university have also been analysing daily urine samples taken from Tian Tian.
Further initiatives may include the development of a joint discovery centre, as well as research on sustainability, climate change and animal conservation and breeding.