The 50-year-old singer was once engaged to Armstrong, and was dating him during two of his Tour de France title wins between 2003 and 2006.
According to the New York Daily News, Crow was interviewed by authorities in late 2011 about Armstrong's activities while they were a couple.
Crow provided information which allegedly incriminated Armstrong in a rumoured doping ring.
Armstrong, who has been stripped of his seven Tour de Force titles, continues to insist that he competed clean.
A representative for Sheryl Crow has declined to comment on the new report.