"Hi, baby, it's me," the transcript read.
Edis said the messages were found in the belongings of Glenn Mulcaire, a private investigator employed by The News of the World, during a 2011 police investigation into alleged phone hacking by the tabloid's employees, the New York Times reported.
The messages were allegedly intercepted in 2006 while the prince was attending the Royal Military Academy Sandhurst.
Mulcaire served jail time in 2007 for hacking the phones of members of the royal family.
Brooks and Coulson are charged along with five other people with conspiracy to illegally intercept voicemails. All of the defendants have denied the allegations.