Photojournalist Gabriele Torsello was seized last Thursday while travelling in a bus in southern Afghanistan.
The kidnappers say they will release Mr Torsello - a Muslim convert - if Abdul Rahman returns from Italy where he was offered asylum earlier this year.
Mr Rahman had escaped a possible death sentence for becoming a Christian.
He had been charged with rejecting Islam and released this March after being deemed mentally unfit to stand trial on a charge of apostasy.
He then fled to Italy where he was offered asylum.
Mr Torsello's kidnappers placed their demand in a phone call to the head of security at a hospital run by an Italian aid agency in Afghanistan.