Tidal is owned my rap mogul Jay Z and has strong ties with artists such as Kayne West, Beyonce and Madonna, which could make it appealing to Apple.
People close to the matter told the Wall Street Journal that talks are ongoing but it may not result in a deal. The streaming service is also said to have been in exploratory talks with other potential partners such as Rhapsody. No specifics for the possible Apple deal were given.
Jay Z bought the Tidal from Swedish technology company Aspiro in January 2015 for $56 million, after squabbles with other services about royalties paid to artists. There are reports that artists receive three times as many royalties per track paid by other streaming services.
Jay Z told Billboard magazine, "Will artists make more money? Even if it means less profit for our bottom line? Absolutely. That's easy for us to do."
The service is also now part-owned by 19 other music artists, including Beyonce, Rihanna, Kanye West, Nicki Minaj and Madonna.
Prince was also an owner of the service and Tidal was the only service to offer the artist's back catalogue after his death in April.
Tidal has been struggling since it was launched in October 2014 and subsequently relaunched in March 2015, as it failed to compete with competitors Spotify, Pandora and more recently Apple Music.
The music-streaming service comes with a hefty monthly subscription rate of $20 for its high-fidelity version, nearly double its competitors. This has limited its mainstream appeal. According to Tidal, it has 4.2 million paying subscribers, which have accumulated over the past year due to exclusive releases.
Spotify in comparison has 30 million subscribers and 70 million free users. The Swedish company has come under fire from artists because it refuses to limit their music to paid subscriptions.
Apple Music in contrast has about 15 million paying subscribers and will be redesigned as part of the fall update to the iPhone software. Apple acquired the streaming service from Beats Electronics, which was founded by rap mogul Dr Dre and former Interscope Geffen A&M Records chairman Jimmy Iovine, for $3 billion in May 2014.
Tidal has also gone through a string of CEOs in the past year and is currently owned by Jeff Toig, former chief business officer of SoundCloud.
Shares in Apple closed at $95.60, 1.27% on Thursday, but were 0.21% down in after-hours trading.