The out-of-contract defender will not be offered a new deal until it is decided whether he was guilty of breaching FA betting regulations.
Last season's club captain will attend the hearing the day before their opening game of the season against Rotherham United.
Stanley assistant manager Jimmy Bell told the Lancashire Telegraph: "Having the hearing on the day before the start of the season might possibly create some issues, having it hanging over you.
"But he is still quite dedicated and he's training with us, there's no reason why he can't play in the first game of the season."
Cavanagh was one of five players charged betting with before a 2-0 home defeat to Bury in May 2008 and their hearing has now been delayed from July 20 to August 7.