She was artificially inseminated earlier this year after attempts to bring her together with male partner, Yang Guang, failed.
The zoo said new scientific tests had given a "strong indication" of pregnancy, but were "too new to be definitive".
Tian Tian also conceived last year, but the pregnancy failed.
Iain Valentine, director of Giant Pandas for the Royal Zoological Society of Scotland, said: "The latest scientific data suggests Tian Tian the giant panda is now pregnant and that implantation has taken place, therefore she may give birth at the end of the month.
"This is all very new and complex science and we still have a bit of time to go yet.
"As like last year, the late loss of a cub remains entirely possible."
The zoo said it had been able to confirm that Tian Tian did become pregnant last year.
However, it said it was most likely that she had reabsorbed the foetus late term.
The two pandas arrived in Scotland from China in 2011.
Tian Tian has had cubs in the past in China, before she came on loan to Edinburgh.
If she does have a successful delivery, it will be the first time a giant panda has been born in Britain.
The panda enclosure at Edinburgh Zoo is due to close to visitors from Saturday ahead of a possible birth.

Since the initial fall-out there has been a legal challenge and a general election.
While everyone waits to see exactly what will happen, Leave voter Paul Austin has told the BBC  why he made his choice and whether, a year on, he would vote the same way again.
Mr Austin lives in North Yorkshire and runs an interior fitting-out business. He has spent 36 years working in the construction industry around the world.
"I was quite an aggressive Brexiteer and my friends were probably sick to the stomach of me trying to persuade them all to vote Leave," he said.
"I wanted limited immigration, not a ban, because I feel that it's totally uncontrolled.
"I'm also still concerned about taxation and VAT. I think the payments we make are very high and that money is going to other countries when it could be used better here."
However, Mr Austin says that on recent trips to the EU he has started to pay more attention to the immigration queue for non-EU passport holders - and is already starting to feel that he is becoming an outsider.
"I think other Europeans are starting to look at us as if we're a bit different and I've now started to back-pedal a bit on how I think about things," he explained.
"I have ended up with more questions than before the referendum."
As well as the continuing political conversations around Brexit, Mr Austin said recent news events had played a significant role in him moving from a clear Leave stance to one where he was less certain.
The recent news story about about baby Charlie Gard and the decisions about his continuing treatment had a powerful impact on him.
"I was quite upset by it and I'm glad his parents were able to get access to the European Court of Human Rights so he can be kept on life support until another group of experts have had time to look at his case," he added.
"But I wonder now about what this means when we leave and if means that other real people won't be able to have one more throw of the dice to have their case heard.
"I'm not saying that had the court not been available judgements would have been unjust, but they would have been unfair because they lost that extra level of consideration."
Another key factor behind Mr Austin's decision to vote Leave was his belief in the potential for the UK to expand its trading base around the world and access more competitive markets.
However, Mr Austin says that since the Grenfell Tower fire last week he now has concerns about how rigorous quality checks will be post-Brexit for imported goods.
"It's made me wonder about the sort of building materials that might be able to come into the country that might not have been tested properly or as well as things are now.
"At the moment we have the European kite mark which means the goods we buy are strongly and intensively vetted and tested.
"I still want more aggressive trading around the world but I'm also starting to think that maybe 40 years of working together to do all this in terms of quality control might be wasted."
By the UGC and Social Media Team
Edinburgh Zoo has said it believes its panda Tian Tian is pregnant and may give birth at the end of the month.
[NEXT_CONCEPT]
It is a year since the UK voted to leave the European Union and Brexit negotiations are under way.