Talks between the two companies are at a preliminary stage and no deal has been agreed, according to people with knowledge, the FT said.
The newspaper added that a source said iHeartMedia, which filed for bankruptcy earlier this year, is hoping that the iPhone-maker will take an equity stake worth tens of millions of dollars. Another source suggested that the tie-up could result in a multimillion-dollar marketing partnership instead of a direct investment, the FT said.
Apple did not immediately respond to CNBC's emailed request for comment.
The FT said that the tech giant declined to comment while iHeartMedia did not respond to multiple requests for comment.
Earlier this year, Apple bought music recognition app Shazam to bolster its music business as the company takes on streaming giant Spotify. Apple's subscription service boasted 50 million active users in May, though the company hasn't offered an official update since. Spotify has 83 million paying subscribers and 100 million or so unpaid users.
Apple is set to report fourth-quarter earnings on Thursday.