Universal Music Group is reported not to be renewing its annual contract to sell its music through Apple's iTunes.
iTunes has 70% of the market in music downloads
The New York Times quoted unnamed executives as saying that Universal had decided to have monthly deals instead.
That would allow Universal to remove songs by some or all of its artists quickly if there are disagreements on terms and pricing in the future.
But the San Francisco Chronicle carried a denial from Apple, which said that talks were still continuing.
"We are still negotiating with Universal," the newspaper quoted an Apple spokesman as saying.
"Their music is still on iTunes and their not re-signing is just not true," he added.
There have been disagreements between Apple and record labels in the past about the pricing and protection of the songs on iTunes.
Apple has stuck to a flat charge of 99 cents per song in the US since iTunes was launched four years ago.
But many of the labels are understood to want to be able to charge more for popular songs and less for songs that they are trying to promote.
There have also been objections to the copy-protection that iTunes uses, which means that iTunes downloads cannot be played on MP3 players other than Apple's iPod.
In February, Apple boss Steve Jobs called on labels to allow iTunes to remove the copy-protection. EMI has since begun to sell "premium" versions of its tracks through iTunes without copy protection.
But some labels have refused to have the protection removed and say that Apple should instead license its technology so that its copy-protected songs can be played on other devices.
Both Apple and Universal have much at stake if their relationship deteriorates.
If Universal pulls its catalogue from iTunes then the store would lose access to record labels that account for one out of every three new releases sold in the US, according to Nielsen SoundScan.
On the other hand, iTunes is by far the most popular download store, with a 70% market share, according to the NPD Group.
Reports of a dispute hit Apple shares on Monday - they closed down 78 cents at $121.26 on Nasdaq, although that was also linked to some disappointment about the first weekend's sales of its new iPhone.