The Ministry of Justice confirmed prisoners are working as call centre operatives at at HMP Oakwood in Wolverhampton and HMP Drake Hall in Staffordshire.
The Sun said the inmates telephone householders and ask them about their financial details on behalf of market research companies.
The prisoners are not allowed to take in writing material and do not have access to the internet at the centres.
A Ministry of Justice spokeswoman said: "All prisoners working in call centres are risk assessed and stringent security measures are in place, with calls supervised and recorded."
Inmates follow a script during calls and are not required to ask members of the public about their valuables.
HMP Drake Hall has been a prison for women since the 1970s, while HMP Oakwood, which is now run privately by security firm G4S, is a prison for men.
The MOJ announced plans to pay prisoners to work in call centres last year to enable them to learn new skills.