Does mama panda at National Zoo have a bun in the oven?

There's growing speculation in Washington at the Smithsonian's National Zoo: Is mama panda Mei Xiang about to surprise the world with a new cub?

Yet, there are a few things a little off with this story.

First, there's no solid proof that Mei Xiang is pregnant, reports CBS News correspondent Chip Reid. Second, we don't even know who the father is. But the signs are there -- Mei's hormones have shot up.

And that's not the only clue that there's a bun in the oven.

One of the National Zoo's most beloved animals spends most of her time these days sleeping, curled up on her right side, sometimes on her left and even sprawled out on her stomach. It's also how zoo keepers think they know Mei Xiang just might be pregnant.

"Other pandas, we can always call them out with a fruitsicle or some honey, but when Mei Xiang is in this mode, there's nothing we can do to get her to move," Brandie Smith, who is in charge of animal care, said.

But that's the thing -- despite how she's acting, it's possible she's not pregnant because giant pandas often experience what's known as a false pregnancy.

Mei Xiang was artificially inseminated twice in April. One of the potential fathers is in China; the other is Tian Tian, a male panda at the National Zoo.

Mei, on the other hand, spends almost all of her time inside in her den, where she's building a nest with bamboo -- another sign she could be getting ready to pop.

She's had ultrasounds, but so far they're inconclusive.

"Mei Xiang likes to keep us in suspense," Smith said. "So as we get toward the end of her pregnancy, she stops participating in the ultra sounds. She makes sure we can't see anything. And then we'll know if she's pregnant when she gives birth."

That's right, we probably won't know she's pregnant until the moment this happens.

Two years ago, Mei gave birth to Bao Bao. It was a cause for celebration because it followed five false pregnancies. For panda fans, Bao Bao has been a star. Millions have watched her grow up on the panda cam, learning to crawl, getting check-ups and playing outside with the occasional adorable tumble.

Pandas are already the most popular animals at the zoo.

"We are panda crazy," as one mom described it, saying it's a family affair.

Now as the possible big day approaches, the crowds are expected to get even bigger, and everyone, including Smith, is hoping for good news for Mei Xiang and this endangered species.

"I always believe 100 percent in my heart that Mei Xiang is pregnant and that we will have a healthy baby panda," Smith said.

If this is a real pregnancy, Mei Xiang could give birth later this month, but more likely in early September.