Experts at Edinburgh Zoo have been monitoring her since she was artificially inseminated on April 13 and it was revealed that "the latest scientific data" suggested she was pregnant in August.
The panda was successfully inseminated last year but lost her cub at late term, something the zoo is wary of again.
Iain Valentine, Director of Giant Pandas for the Royal Zoological Society of Scotland, said:
"Giant panda Tian Tian is now past her due date and the evidence suggests that this may be bad news. She is still displaying some of the behaviours of a pregnant panda, but the scientific data from the urine analysis of her hormones is becoming more atypical. There is still a chance she will give birth to a live cub as her progesterone levels have not yet returned to base.
"I must stress, as there has been a lot in the news recently about pandas 'faking' it, that this was definitely not a pseudo or phantom pregnancy. The results of cutting edge scientific analysis have shown that, across the entire pregnancy, Tian Tian had the profile of a pregnant panda likely to carry to full term. We are working with the of the very best panda experts in the world and they were all in agreement.
"The scientific data extracted by analysing hormones and proteins in her urine was a text book example of what we wanted to see. However, at the very end of last week there were one or two results from the hormone tests that were atypical and that was the first sign something might be amiss. Although it is still very new, the scientific data does suggest that the last point she should have gone into labour was over the weekend, unfortunately this did not happen. "
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.