Many Apple rumors center on alleged acquisitions, which is somewhat odd given that Apple, as opposed to companies like Google and Microsoft, is much more selective when it comes to corporate acquisitions.
All that said, word spread in 2003 that Apple was looking into acquiring the Universal Music Group record label. At the time, sources from both CNET and the LA Times reported that Apple had engaged in "very preliminary" discussions regarding such a deal. Much like the Jay-Z rumor, however, there wouldn't be much for Apple to gain in managing its own record label. To be fair, this rumor did make a bit more sense because it preceded the launch of the iTunes Music Store.