It is said to have concluded that many Muslim prison chaplains were under-equipped for counter-radicalisation work, "sometimes because they lacked the capability but often because they didn't have the will".
Prisoners at more than one jail were encouraged by chaplains to fund-raise for Islamic charities that had links to terrorism, according to the report, which warned that lax controls and senior level failings had allowed the problems to occur.
The Times reported that jails in England and Wales held 12,328 Muslim inmates at the start of 2016.
Convicted terrorists numbered 131 and a further 1,000 were deemed vulnerable to radicalisation.
Muslims make up 4.8% of the population but 14.5% of prisoners.
About 100 Muslim chaplains are employed full time in jails on salaries of up to £40,000.