Update: Windows 9 is now known as Windows 10. Want to know more about when you can get your hands on it? Check out our in-depth Windows 10 release date page
Neowin also claims the tool is being targeted for the final release of Windows 9 (currently codenamed Windows Threshold), expected in spring 2015.
The reports are corroborated by The Verge, whose sources claim the tool is gradually getting better every couple of weeks along its journey to an eventual roll out within Windows 9.
So what form will Cortana take within Windows 9? Well Neowin says it is a "simple app that opens up the personal digital assistant where you can then either type in your question or ask verbally inside a smallish window. It's not a full-screen experience like you see on Windows Phone."
However, it's clear that could alter significantly between now and Windows 9's release date. Microsoft is expected to launch a preview release before 2014 is out.
The reports follow speculation earlier this month hinting that Siri may make the move from iOS to the Mac OS X desktop software, based on an Apple patent filing from 2012.
Are we all set for the Siri vs Cortana battle to move to the desktop arena?
- Is the new OS any good? Read our hands on Windows 10 review to find out