Bloomberg's Mark Gurman made the claim in his Power On newsletter, in which he alleged the two tech giants were meant to begin the support "weeks ago".
If true, it means Apple will start selling Sony's virtual reality headsets and give Vision Pro users access to more games.
Meanwhile, Sony is reportedly considering a new handheld console to rival the Nintendo Switch.
The Japanese tech giant has created portable devices in the past, such as the PlayStation Portable (PSP) and the PlayStation Portal Remote Player for its PlayStation 5 (PS5) console, but a recent report by Bloomberg claimed the firm is in the early stages of developing a new similar device that will enable gamers to play PS5 games on the go.
The outlet claims the "idea builds on the PlayStation Portal", the eight-inch device released last year that allows users to play compatible video games over an internet connection.
The publication did, however, note that Sony could be years away from launching such a device and that it may not even see the light of day.
As well as the Nintendo Switch, which was released in 2017, it is believed it could rival something similar from Xbox, with Microsoft allegedly "working on prototypes".