The California state Department of Corrections and Rehabilitation told local outlet CBS 8 that Menendez was in a “fair condition”, but that it could not give further details.
The brothers, who have been behind bars for 35 years, were resentenced in May to 50 years to life in prison for the killings of Kitty and José Menendez, in 1989.
They were previously serving life without the possibility of parole.
But earlier this year, a Los Angeles judge determined Erik, 54, and Lyle, 57, did not pose an “unreasonable risk” if they were released. The judge added that the brothers had “done enough” while in prison to merit a change of sentence.
The pair’s new sentence made them eligible for parole consideration due to their young ages when their crimes were committed.
The brothers’ lawyer Mark Geragos called for Erik Menendez’s release in a TMZ interview, making reference to his client’s health.
“I just think he should be parole furloughed, I think is the proper term, and he could be medically furloughed in advance of the hearing so that he can work with the parole attorney and get up to speed and be ready and do it and give it his best shot,” Mr Geragos said. “I think that it’s the only fair and equitable thing to do.”
The brothers’ parole hearing is scheduled for 21 August.
The pair went through two trials before being convicted in the 1990s. They have claimed the murders were in self-defence. Prosecutors contended that the brothers were spoilt young men who killed their parents for financial gain.