"To date you have reportedly declined due to religious reasons/conflicts with your Islamic faith," Clements wrote.
The letter also notes that on February 25, 2011, al-Turki's sentence was reduced to six years to life.
CNN has not received a response to its requests for comment from al-Turki's lawyers.
In light of the renewed attention on his case, al-Turki was removed this week from the rest of his prison's population, according to the state's department of corrections.
Late prisons chief described as 'amazing man'
Clements had been chief of Colorado's prison system for a little over two years. He took the job in January 2011 after working for 31 years as part of Missouri's Department of Corrections.
In his time in Colorado, he'd made a big impression.
"He was an amazing man, an amazing man," Alison Morgan, spokeswoman for Colorado's Department of Corrections, said Thursday. "An inspirational leader."
He was killed around 8:45 p.m. MT (10:45 p.m. ET) Tuesday, as he answered the door of his Monument, Colorado, home.
Since then, investigators had said they knew very little about who might have pulled the trigger.
Some witnesses, though, said they saw a man driving a vehicle -- possibly a Lincoln Continental or a two-door Cadillac -- away from the neighborhood a short time after the shooting. Others reported seeing a black, boxy vehicle with its engine running but no one inside on Clements' street.
Asked Thursday whether the prison chief's killing may have been a professional hit, Presley from the El Paso County, Colorado, Sheriff's Office said, "We don't have any specific information that would lead us to that."
The central Colorado county sheriff office's major crimes unit has received more than 100 solid tips about the incident, including a growing number of witnesses describing a black car then in the area.
Meanwhile, the mourning continues for Clements. His funeral will be held Sunday, Gov. John Hickenlooper's office said, and he'll be remembered at a public memorial service in Colorado Springs the next day.