Billboard magazine reported on Thursday, citing sources.
Iovine is best known as the co-founder of Interscope Records, a rap music pioneer that branched out to include artists like Lady Gaga and U2.
Iovine's departure is likely timed to his Apple shares fully vesting, according to Reuters.
The former Interscope CEO joined Apple in 2014 after the iPhone maker bought Beats Electronics, the audio technology firm co-founded by influential hip-hop producer Dr Dre and Iovine, for $3 billion.
Apple declined to comment.
The company told Billboard in September it had 30 million Apple Music subscribers.