A person familiar with the matter confirmed the talks with The Associated Press but was not authorized to speak publicly and spoke on condition of anonymity.
In October, Lala co-founder Bill Nguyen demonstrated to the AP a working model of an application the company had developed for Apple's iPhone.
The app, which is not available to the public, allows users to buy the right to stream songs from a digital locker for an unlimited time on their iPhones for just 10 cents each.
The song quality is lower than what Apple's iTunes songs offer, but "intelligent caching" allows tracks to load and play in seconds, with playback possible even outside of cell phone coverage. The model undercuts prices charged on iTunes, where songs generally cost 69 cents to $1.29.
Nguyen described the concept as the start of "the end of the MP3."
A key reason for Apple to buy Lala is to keep Nguyen and the development team on board, the person said.
Representatives from Apple and Lala did not immediately return messages seeking comment.
Lala, a private company based in Palo Alto, Calif., was launched in 2006 with $35 million in venture capital from Bain Capital LLC, Ignition Partners and Warner Music Group Corp.
In October, Lala became a part of Google Inc.'s new music search feature that put links to free song plays at the top of search results. Lala, which has deals with all the major recording companies, provides music for about half of the links that appear.
Lala also debuted a service that month that allows Facebook friends to send each other 10-cent Web songs to stream on their pages or 90-cent song downloads in the MP3 format.
Lala began as an online CD-trading site but relaunched in October 2008 as a music retailer that sold song-streaming rights for 10 cents and MP3 downloads for an extra 79 cents.