Apple Music is already available on Android and works well, but you can't cast from it.
Apple is working on updating the app at the moment; the recent 2.8 update added support for Chromebooks.
Apple Music was initially launched only for Apple devices, and although support was eventually extended for Android, it still tends to work best with Apple hardware.
However, apart from the Apple iPhone series, the HomePod, and the Apple TV range, even Amazon Echo and Fire TV devices in the US allow Apple Music linking. We could soon see support for the music streaming service extend to Google Chromecast devices as well, according to a new report based on code discovered in Apple Music's Android app.
According to the report, various lines of code have been found in the Apple Music app for Android that point to coming support for Google Chromecast devices. This would allow users to directly cast audio from Apple Music to select Google hardware. Last month, reports had also suggested that Apple Music could be coming to Google Home devices through the app, although this hasn't rolled out yet.
Apple appears to be taking a more user-friendly approach with its Music streaming service, likely in an effort to keep its subscriber base high in the face of mounting competition.
With the recent launches of Spotify and YouTube Music in India, Apple extending support to Google devices and improving its Android app could be necessary in keeping its Android user base happy.
However, this doesn't indicate anything firmly, and indeed we could see nothing come from this at all. Any integration with Google devices would nonetheless be a welcome step from the Cupertino-based electronics giant.