The report, published by Digital Music News, quotes sources "with close and active business relationships with Apple", and says terminating iTunes downloads was a case of “not if, but when”.
It goes on to say that sales from downloads are declining, as we know, and will 'only' be worth $600 million in 2019, compared to peak iTunes revenue of $3.9 billion in 2012.
Naturally the movement of consumers from downloading to streaming is central to this thinking. Apple Music has amassed 13 million subscribers since July 2015 and the total number is expected to hit 20 million by the end of 2016. According to the report, revenues from its streaming service are expected to surpass the peak iTunes download revenue figure by 2020.
Should Apple bow out of the downloads market, it could do so on a territory-by-territory basis, separating those that haven’t quite caught the streaming bug with those that have. The USA and UK, plus parts of Europe and Asia, would be 'tier 1', and the first to see the end of music downloads on the iTunes Store.
However, Apple was - for once - quick to comment on the rumours. Apple spokesman Tom Neumayr told BuzzFeed News (somewhat matter-of-factly): “This is not true."
But that's not to say there isn't some truth in the rumours. While downloads are still big business compared to Apple's streaming revenues, the mass-market appears to be only heading in one direction.
Streaming revenues in the US overtook revenues from physical sales for the first time last year, and made-up 33 per cent of total industry revenues in the first half of 2015 - up from 26 per cent the previous year. Revenues from downloads fell 4 per cent over the same period.
In the UK, the Official Charts Company reported 11.5 billion streams in the UK during the first half of 2015, a rise of 80 per cent on the same period the previous year.
Could the iTunes Store soon go the way of the iPod?