Citing two people "familiar with the company's explorations", The New York Times reported at the weekend that Apple is testing the watch at its Cupertino, California, headquarters.
There is plenty of competition in the growing wearable technology sector, including Sony having launched a smartwatch last year and Pebble, the startup that raised over $10m on Kickstarter, starting sales of its e-paper watch last month. Then there is the Nike Fuelband and Jawbone Up, which are used for fitness and monitor the human body in real time.
But The New York Times says that Apple's watch - already being dubbed the 'iWatch' - would differ to rivals by running the iOS operating system that powers iPhones and iPads, as well as feature glass that "can curve around the human body".
Corning, the maker of the tough Gorilla Glass that is used on the iPhone, last year unveiled Willow Glass - super-thin and ultra flexible glass for electronic devices.
Pete Bocko, the company's chief technology officer, told The New York Times that this could be used to wrap around a human wrist, including on a watch, but it remains a difficult challenge.
"The human body moves in unpredictable ways," he said. "It's one of the toughest mechanical challenges."
Last month, a Chinese technology site claimed that Apple was working on a watch with a 1.5-inch display and featuring a Bluetooth connection to link with an iDevice. The report said that the watch would support Apple's Siri voice assistant, and it coud launch within the first half of 2013.
Sarah Rotman Epps, a specialist in wearable technology at Forrester, said that Apple has "made a lot of hiring in that area", but doubted that the iWatch is imminent.
She told The Times: "Apple is already in the wearable space through its ecosystem partners that make accessories that connect to the iPhone. This makes Apple potentially the biggest player of the wearables market in a sort of invisible way.
"Over the long term wearable computing is inevitable for Apple; devices are diversifying and the human body is a rich canvas for the computer. But I'm not sure how close we are to a new piece of Apple hardware that is worn on the body."
However, The Wall Street Journal also claims that Apple is experimenting with a smartwatch, and has even discussed the device with Foxconn, its main manufacturing supplier.
> Wearable and washable technology steps closer to reality
> CES 2013: Best of the US tech show - images