Tian Tian was artificially inseminated in April after she and her intended partner Yang Guang failed to mate naturally.
Edinburgh Zoo said that while tests indicate she has conceived, it is not yet known whether she is pregnant as the embryo is not implanted into the womb immediately in pandas.
If all goes well, Tian Tian could become pregnant in 20 to 30 days and give birth in late August.
Iain Valentine, director of giant pandas for the Royal Zoological Society of Scotland, said: "It is still way too early to make any definitive predictions. Tests do indicate that Tian Tian has conceived, but not that she is pregnant.
"Pandas practise delayed implantation, so at this stage the embryo is still in diapause, or rest, so technically pregnancy has not happened yet.
"There are many more significant developments still to take place. Timings are all approximate, but we have just seen a secondary rise in progesterone in early July, so if all still remains on track, in 20 to 30 days, pregnancy will commence.
"After this, if successful, Tian Tian would give birth roughly around late August. As you can see, there is a long way to go yet, so we would urge everyone not to get too excited at this early stage.
"Tian Tian is in great health; very relaxed, at a great weight and eating well, and keepers and scientists continue to monitor her."
Their hopes of a pregnancy follow last year's disappointment when the pair did not mate. Although Tian Tian was artificially inseminated, she lost her foetus at late term.
Tian Tian (Sweetie) and Yang Guang (Sunshine) are the first giant pandas to live in the UK for 17 years.
The animals, now both aged 10, arrived on loan from China in December 2011 and will remain at Edinburgh Zoo for a decade.
The zoo said the panda breeding programme can play an important role in conservation.
The panda gestation period is typically five months and one or two cubs will be born.
They enter the world blind, hairless and unable to move - making them entirely dependent on their mother for survival for their first weeks.