Are we just over a week away from seeing what an Apple HDTV will do and look like? There’s a growing number of rumors suggesting just that.

Jonathan S. Geller, the founder of BGR, tells us he has learned from a “trusted source” that Apple will demonstrate a new Apple TV OS at the World Wide Developer Conference (WWDC), which opens June 11. The new OS is said to be more feature-rich than the current version, and is designed to run on the new Apple HDTV.

“Our source believes Apple won’t actually show its physical TV at WWDC,” said Geller on his site, “but it’s certainly possible.”

A few weeks ago we told you about rumors that Apple may introduce the iPhone 5 at the WWDC. Could they possibly introduce both at the same conference. That certainly would be exciting, eh? But it doesn’t seem likely. One would expect that Apple would want to host their own event for such a thing.

However, one thing that Geller mentions is that Apple will want to enlist other companies to make third party accessories (and presumably, apps) compatible with the new TV. To do that, Apple may need to introduce the Apple TV OS early to give those companies a heads up, so when the TV is actually launched, there will be third party products ready for use with it right away.

Forbes reported yesterday that Piper Jaffray analyst Gene Munster is holding firm to his prediction that Apple will launch an HDTV. We told you last week that Munster expected the new TV to sell for between $1,500 to $2,000 and be available in sizes from 42 inches to 55 inches. Forbes says that Munster expects the TV to be introduced before the end of the year, and said they will launch it about 6 months later.

A variety of other rumors that we have already reported on continue to make the rounds and seem to be strengthening. From the name, perhaps iPanel or iTV, to it’s features, such as Siri, gesture control, and video conferencing.

Apple has been mostly mum about all this, of course. The company is famous for holding on to its secrets. But the Washington Post is reporting that Apple’s CEO, Tim Cook, confirmed that “television is an area of ‘intense focus’ for the company” during an interview last week. That’s a pretty strong hint of where Apple is going.

If Apple tortures us by waiting until the very last day of the WWDC, then the latest we would hear about the new Apple TV OS would be June 15. But that’s only if this particular rumor bears fruit. We may get to no Apple TV joy at all – we’ll just have to wait and see.