Twitter has weighed up deals worth billions of dollars and has also considered buying music-streaming service Spotify and internet-radio provider Pandora Media Inc, the newspaper.
SoundCloud is a platform that enables people to upload, record, promote and share their music and other audio files.
The company has aggressively expanded its capabilities to carry multimedia content. Last year, it acquired "We Are Hunted," a three-person music streaming-startup from Australia.
SoundCloud declined to comment on the deal while Twitter did not immediately respond to an email seeking comment outside regular U.S. business hours.
Twitter's renewed interest in music-streaming companies comes after Apple Inc acquired Beats, the headphones and music-streaming firm founded by Jimmy Iovine and Dr. Dre, for $3 billion.
The Beats deal was seen as Apple's effort to jumpstart an uneven attempt to make headway in music streaming, the fastest-growing segment of the market, as iTunes sales decline.
Pandora Media and Spotify have raced ahead while Apple's eight-month-old iTunes Radio has not made much of a dent.