The Church urged the singer to try its Narconon drugs programme, which it claims has helped hundreds of people kick their addiction, according to the Sunday Mirror.
Winehouse is reportedly considering joining the group, which already counts Tom Cruise and John Travolta as members.
"She had a call from the celebrity branch of the Church Of Scientology. She thinks they got her number through one of the American music producers who worked on her Back To Black album," said a source.
It was recently claimed that Tom Cruise has given Kirsten Dunst a Scientology manual to help her through tough times.