This story has been updated with Beats Electronics' response.
Citing people familiar with the deal, the FT reports that the deal could be announced next week, but noted that some details have not yet been agreed and that the deal could still break down.
The rumor comes one day after the head of public relations at Apple, Katie Cotton, stepped down, to spend more time with her family.
Both Apple and Beats Electronics declined to comment on this story when contacted by TheStreet. A purchase, however, would expand Apple's reach into the music hardware market and also provide a further injection of cool into the iPhone maker's brand.
An acquisition of Beats Electronics, though, would mark a significant shift in Apple's M&A strategy, dwarfing its previous purchases. Apple's largest acquisition to date was its $390 million deal for Israeli Flash Memory specialist Anobit in late 2011.
Beats Electronics' music streaming app, Beats Music is currently ranked eighteenth in Apple's App Store under the music section.
Apple shares, which closed down 0.18% during Thursday's trading, slipped 0.65% to $584.06 after market close.
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--Written by James Rogers in New York.
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