The British musician, who had long struggled with drug and alcohol addiction, was found dead of unknown causes at her London home on Saturday. She was 27.
It was not clear how finished the tracks are. Winehouse released only two albums in her lifetime, but she had been in and out of the studio over the past few years. In July 2010 she said a new album would appear within six months, but it was never finished.
The Guardian newspaper quoted an unnamed spokesman "close to" record label Universal as saying Winehouse had left the "framework" of about a dozen songs.
There would certainly be an appetite for new material. Two days after her funeral, dozens of mourners continued to gather outside her home in north London, leaving flowers and taking photos.
Sales of Winehouse's music have soared since her death. In the U.S., digital sales of her tracks have risen by 2,000 percent in the past week, according to Nielsen Soundscan, and "Back to Black" is set to re-enter the Billboard album chart at No. 9.
The Associated Press contributed to this report.