It was one of a number of measures recommended in a review of inmates’ contact with family and friends by HM Inspectorate of Prisons (HMIP).
It said a pilot should be carried out allowing “risk-assessed” and supervised prisoners to have family contact through social media and/or video-chat service Skype.
The findings should be evaluated and the results published, HMIP added.
The new paper also called for inmates to be allowed to receive incoming calls from their children or their carers on a “risk-assessed basis”.
Prisoners cannot routinely take incoming calls and rely on phones provided by jails to call up to 20 numbers which have to be listed on their account.
They pay for calls using either earnings from work in prison or money sent in by family.
Surveys suggest that approximately half of men and women in prison report having children under the age of 18.
The HMIP paper said: “When properly risk-assessed and supervised, we would expect children and those caring for them to be able to make calls to their parents in prison.
“However, even within the female estate this is rarely achieved.”
The watchdog also recommended the rollout of in-cell phones to existing prisons should continue “as resources permit” while all new prisons should incorporate them.
A small number of prisons have in-cell telephones.
They are subject to the same security processes as wing phones and calls can only be made to numbers from the prisoner’s account, but they enable inmates to make phone calls at any time during the day when they are in their cell.