The paper reports that the two parties have failed to reach a deal because Microsoft's strategy of charging for all content on Xbox Live is incompatible with the BBC's public service remit.
Apparently Microsoft only wants to offer its users access to platforms it can charge for, as this is the business model it is pursuing, say sources close to the BBC's Future Media and Technology department.
For example, Xbox owners who want to access the Sky Player on their consoles have to pay for an Xbox LIve Gold subscription as well as a Sky subscription.
But the BBC cannot charge the British public for access to the iPlayer as it is already included in the licence fee.
Nintendo's Wii and Sony's PlayStation 3 both offer free access to the iPlayer. Nintendo recently relaunched its Wii catch-up TV service, which now has its own dedicated BBC iPlayer channel.