This rumour doesn't seem particularly far-fetched, especially, as 9to5Mac points out, Apple opened up Lightning headphone specs to manufacturers last June, through its Made-for-iPhone licensing program.
The first example of Lightning-connected heapdhones - Harman’s JBL Reflect Aware headphones - were shown at the Consumer Electronics Show in Las Vegas in January this year.
One of the apparent advantages of using Lightning for audio is that it can draw power from the iPhone itself, without the need for an internal battery.
Using wireless headphones would continue to be simple, as there would be no specific compatibility issues with the iPhone.
Plus, wireless headphones are compatible with Apple's full range of products including the Apple Watch and the Apple TV (whose remote control has a Lightning charging port).
Although this will cause initial complaints if it were to launch, headphone companies will likely adapt. Apple has already sold twice as many iPhones with a Lightning connector, compared to previous models.