The 32-year-old is being held without bail at Twin Towers Correctional Facility as he awaits trial after pleading not guilty to the deaths of filmmaker Rob Reiner and Michele Reiner.
And according to reporting by the Daily Mail, Greene has been the only person to visit Nick at the Los Angeles jail since his arrest.
She took over the case after defence lawyer Alan Jackson stepped down before Nick's court hearing in January. Kimberly appeared alongside Nick in court on February 23 when he formally entered his not guilty plea to two counts of first-degree murder.
Nick is being held under strict supervision conditions.
Former Los Angeles County sheriff Alex Villanueva said inmates in high-profile cases are typically isolated from the wider prison population.
Villanueva told the Daily Mail: "Any type of case like this, a high-profile case, causes the department to place the inmate in what's called administrative segregation, designed to prevent the inmate from being hurt by other inmates."
Villanueva also said the clothing Nick wore during his most recent court appearance suggested he was being monitored closely by prison staff, adding: "They get mandatory checks every 15 minutes at a minimum, 24/7. Some have to remain alone at all times because they're a danger, not only to others, but to themselves too.
"They want to hurt themselves, or they want to hurt somebody else."
According to Villanueva , the "suicide gown" that has been previously worn by Nick in court indicates he may be in what is known as mental observation housing within the jail.
Twin Towers Correctional Facility has previously housed several high-profile inmates, including Paris Hilton, Harvey Weinstein and Robert Downey Jr.
Beverly Hills defence lawyer Adam Michael Sacks has spoken about the conditions at the jail in comments to Page Six.
Sacks told the outlet the facility is "disgusting".
He added said many of his former clients had pleaded to be released from the prison and said his clients "begged for bail" when he visited them at the facility.
Nick appeared in court for an arraignment last week wearing a brown jumpsuit and shackles.
During the hearing he spoke with Kimberly through a plexiglass barrier.
Nick was arrested after Rob Reiner, 78, and his photographer wife Michele Reiner, 70, were found stabbed to death in their home in December.
The Los Angeles County Medical Examiner's Office confirmed both deaths were caused by "multiple sharp force injuries" and ruled them homicides.
Nick had struggled with drug addiction and had spent time in rehabilitation before the deaths.
He had also previously been diagnosed with schizophrenia.
Nick's siblings Romy Reiner, 28, and Jake Reiner, 34, have not attended any of the court hearings related to the case.
Nick is next scheduled to appear in court on April 29.
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