The attorneys also included a letter from ordained Jewish clergyman Cantor Michael Zoosman who has been in touch with Gonzales, in their request to the Governor.
"There has been no doubt in my mind that Ramiro's desire to be an altruistic kidney donor is not motivated by a last-minute attempt to stop or delay his execution," Zoosman wrote, according to the Associated Press.
"I will go to my grave believing in my heart that this is something that Ramiro wants to do to help make his soul right with his God."
The inmate's lawyers also made an additional request for a 180-day postponement to the Texas Board of Pardons and Paroles in relation to the kidney donation.
It's not the first time a request was made on behalf of Gonzales to donate an organ, with his first solicitation rejected by the Department of Criminal Justice earlier this year.
There was no explanation behind the decision to decline his request, however, Gonzales' lawyers argue that it was due to his "imminent" death.
The request to reschedule Gonzales' execution comes after his date to receive the lethal injection on November 17 last year was postponed.
Due to ongoing religious rights issues in Texas regarding inmates not having the right to be "touched" or "prayed out loud for" by their spiritual adviser, Gonzales' death was delayed.
Since then, the Supreme Court of the United States has ruled that spiritual advisers are permitted in the execution chamber and can touch and pray for inmates receiving the death penalty.
Gonzales' lawyers have requested that the inmate be accompanied by a spiritual adviser during his time of death, with a trial set to affirm that request scheduled for Tuesday, central daylight time.
'This is part of my atonement'
Keri Blakinger, a reporter for The Marshall Project, visited Gonzales last week for a tell-all, hour-long interview.
He told her that he had made the offer as 'atonement" for his crime.
"This is part of my atonement. When you take something so precious from the world, how do you pay that back? You don't. You spend all these years trying to make restitution," he said.
"He said, 'How can I give back life? This is probably one of the closest things to doing that. I don't want to say it's saving someone's life but it's keeping someone from dying'."
Blakinger said that in all her years of covering death row inmates, Gonzales' proposed organ donation was unique.
"I don't know if the logistics of this will work out for him. He's having trouble getting the approvals through the state," she said.
"He can't just sign over his organs after he dies because the death drugs will poison him. So he has to do a live kidney donation before he is executed."
