A lawyer is calling for Lord Carey to be investigated following the release of files by police under a freedom of information request, according to The Times.
The files include detailed Church of England internal reviews of the case of disgraced bishop Peter Ball, 84, jailed for 32 month last October after pleading guilty to misconduct in public office and indecent assaults on 18 young men between 1977 and 1992.
According to the files, Lambeth Palace received six letters after Ball was cautioned in 1992 revealing that he encouraged victims to pray naked, perform sex acts in front of him and share his bed.
He received a caution in 1993 for gross indecency, after he had been made Bishop of Gloucester in 1992. He resigned as bishop yet was still allowed to return to ministry, even though the Church knew there were other survivors who had come forward.
He was allowed to take services in top public schools and attend Scout functions. Evidence which indicated he could be a serial sex offender was not passed on to police.
Officials at Lambeth Palace reviewed the letters in 2009 and noted that had the evidence in them been passed on in 1993, Ball might have been convicted of serious sexual offences as opposed to merely being cautioned.
One victim, Neil Todd, committed suicide in 2012. The letters were finally given to the police that same year.
The also indicate that Ball associated with other sex offenders in the clergy, that he was investigated in 2008 for being part of a suspected paedophile ring and that he helped other priests accused of sex abuse, including failing in 1978 to take action against a paedophile priest.
The present Archbishop of Canterbury Justin Welby has ordered an independent review of the Ball case. Judge Lowell Goddard's Independent Inquiry into Child Sexual Abuse is also examining the case.
One of the victims' lawyers has called for police to look into whether senior church leaders, including the former Archbishop, perverted the course of justice or committed misconduct in public office, The Times reports.
Lord Carey's spokesman declined to comment but said Carey, who was Archbishop of Canterbury between 1991 and 2002, was cooperating fully with Welby's review. When Ball went on trial last year, Carey denied that his correspondence with the Crown Prosecution Service at the time of Ball's caution in 1992 amounted to attempts at a cover-up.