The Wall Street Journal cites "people briefed on the company's plans" as saying that the new Android-powered system would be marketed under the Google brand.
The multi-room entertainment system is said to be in development at the Android team within Google, and it could be extended to the streaming of other content beyond music.
According to the Journal, Google started testing the product six months ago and could look to launch the hardware at some point in 2012.
The Rupert Murdoch-owned paper has a strong track record in predicting Google's new products, after it first disclosed the Google TV software plans back in 2010.
If this latest report is true, it would mark a seismic shift for Google into designing and producing electronic goods branded under its own name for the first time.
The company has previously focused on creating operating systems such as Android for mobile and tablet devices, along with Google TV for television brands, and then allowing other firms to actually produce the end products.
It is thought that the Google-branded wireless streaming solution would be a competitor to Apple's AirPlay, which allows iOS devices to send content to the TV via the Apple TV product, or stream content to AirPlay-enabled docks and speakers.
Google is widely expected to take big strides into hardware manufacturing this year, mainly as part of its $12.5bn (£7.7bn) takeover of smartphone and tablet maker Motorola Mobility.
Alongside the rumoured home entertainment system, the firm is thought to be working on its first ever branded tablet computer for launch in 2012.
A report also emerged this week that Google has developed a pair of Terminator-style prototype glasses, which would use augmented reality to provide real-time information in front of the user from services such as Google Maps.