The acquisition, alongside Jay Z's portfolio of popular musicians and friends, would beef up Apple Music, sources told the Journal. Still, the talks may not result in a deal, and the terms of the deal are unknown, the Journal said.
A Tidal spokesman denied that Tidal executives had held talks with Apple, according to the Journal. Apple declined to comment to CNBC on the report.
At $19.99 per month for its high-fidelity version and $9.99 for standard sound quality, Tidal focuses on richer, "lossless" musical sound. It has said it has 4.2 million paying subscribers, according to the Journal.
But the company has seen turnover among executives, the Journal reported.
Such an acquisition would come as Apple has invested more deeply in its music platform, announcing a redesign at a developers' conference earlier this summer. Apple Music debuted one year ago, after Apple had purchased Beats Electronics, founded by rapper Dr. Dre the year prior.
Clarification: The article has been updated to reflect the different price points for Tidal's service.
— CNBC's Josh Lipton contributed to this report.