This would allow officials to investigate whether prisoners were "trying to run a business", contacting or harassing victims, or planning further crimes.
Mobile phones were banned in all New Zealand prisons, which had signal-jamming technology to prevent incoming and outgoing calls.
Asked whether this meant signal-jamming was not working, Mrs Tolley said the proposed amendment was a "back-up".
"Jamming is generally pretty effective. But there are the odd black spots, and prisoners would be the first ones to find them. We've just got to keep one step ahead of these guys."
The amendments would be put before a select committee, but Mrs Tolley expected telecommunications companies to co-operate because they already released details to organisations such as the Serious Fraud Office.
The minister was also seeking to extend the amount of time that recordings of prisoner's landline calls could be held by the department from six months to two years.
The Corrections Amendment Bill attempts to make prisons more cost-effective and also to remove barriers to managing prisoners.
The minister has asked for a law change that meant inmates separated because of a risk of self-harm would face mandatory strip-searches when moved to an at-risk unit.
This was a response to a Court of Appeal decision in April which said prison officers could only search an inmate if they could "reasonably conclude" that a search was necessary for finding contraband.
Howard League for Penal Reform spokesman Jarrod Gilbert said Corrections would have to be careful that the new rules did not further unsettle prisoners who were vulnerable to self-harm.
Corrections Association of New Zealand president Beven Hanlon was concerned about an amendment to allow non-custodial staff to read prisoners' mail. "I don't think it should be left to some contractor to do without proper security clearance and checks."
The committee was calling for public submissions on the new amendments before July 27.
UP FOR DEBATE
Law changes proposed by Corrections Minister:
* Phone companies required to provide access codes to prisoners' mobile phones.
* Authority to read prisoners' mail extended to non-custodial staff.
* Prisoners' drinking water to be of a standard similar to public drinking water.
* Mandatory strip-searches of inmates moving to a separate unit because of self-harm risk.
* Recordings of prisoners' phone calls can be kept for 2 years, instead of 6 months.