On Wednesday, CNET‘s Greg Sandoval reported that Apple (AAPL) had persuaded EMI and Warner Music (WMG) to be part of its widely anticipated — but as yet unannounced — streaming music service (see here).

Now, in an item that moved on the Bloomberg newswire late Thursday, Andy Fixmer and Adam Satariano report that Sony Music (SNE) has also come on board, and that Universal Music — the largest of the big four music labels — is “close to a deal.”

Apple, through iTunes, already operates the world’s largest music store. In the next iteration of iTunes, according to widespread reports, high-quality copies of the music labels’ songs would be stored on Apple’s servers. Then, with the users’ permission, Apple would scan their Macs or Windows PCs to see what songs they owned. Users would then have free access to those songs on Apple’s servers whenever they wanted and on any device they owned.

Amazon this year launched a similar service and Google is testing another (both were reviewed by Walt Mossberg in Thursday’s
Wall Street Journal
). But neither Amazon nor Google was able to come to terms with the music labels, which meant that to get the same streaming access, users would first have to upload their entire music libraries, a process that can take days.

With the big four labels in place, Apple could be in position to unveil the new iTunes at its Worldwide Developers Conference, which begins in San Francisco on June 6.