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."
Mr Valentine said there were "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," he said.
"If successful, Tian Tian would give birth roughly around late August.
"There is a long way to go yet, so we would urge everyone not to get too excited at this stage. Tian Tian is in great health; very relaxed, at a great weight and eating well."
Tian Tian became pregnant last year but in October it was announced she had lost the cub.