That decision is expected tomorrow after Reid gives evidence.
Murray says the calls are privileged because she was acting as Reid's lawyer at the time.
Crown prosecutor Anna Longdill says the subject of the calls are not legal advice and therefore are not confidential.
Much of today's hearing was taken up with legal arguments about what can or cannot be used as evidence in the trial and reporting has been limited by suppression orders.
Murray is being aided in court by her former boss Barry Hart, who was struck off the Law Society's register after a 46-year career.
Hart is acting in a role known as a McKenzie friend. He is allowed to pass notes, suggest questions and provide general support to his former junior lawyer.
The defended hearing, before Judge Collins, is expected to last five days and to hear evidence from high-security prisoners, including Reid.
Reid is serving a 23-year sentence for raping and killing deaf woman Emma Agnew in Christchurch in 2007, and the rape, attempted murder and robbery of a 21-year-old student in Dunedin nine days later.