CCA spokesman Steven Owen said the company is taking appropriate steps to remedy staffing problems at the prison and is committed to reimbursing taxpayers for any unverified hours.
CCA's contract with Idaho ends on June 30, 2014.
"We have delivered exceptional value to Idaho's taxpayers through cost savings, and we've also provided outstanding rehabilitation programming to the inmates entrusted in our care," Regens wrote in the letter.
It's not clear, however, whether Idaho's $29 million contract with CCA represented an actual cost savings. An investigation by The Associated Press in 2012 showed it would likely cost the Idaho Department of Corrections the same amount of money or less to have state employees run the facility.
Idaho Department of Correction Director Brent Reinke has asked the state Board of Correction at least twice if his department should examine whether it would be cheaper for the state to run the prison, but both times he was rebuffed.
The Idaho Board of Correction had the option to extend CCA's contract for two more years but decided in June against it. Instead, the state will issue a formal request for proposals later this year.
At the time, the board didn't rule out the possibility that it would select CCA to run the prison under a new contract.
Regens, however, said the company does not intend to submit a proposal.
"We will focus our efforts during the remainder of the contract term on ensuring the facility continues to operate in a safe and secure manner," he said in the Wednesday letter. "We will work closely with the department to ensure a smooth and orderly transition."
CCA has acknowledged that its employees filed staffing reports with the state that incorrectly showed it had the contractually required number of guards on duty during several months in 2012.
Owen, the company's spokesman, said the unverified hours were only a fraction of total staffing requirements at the prison. The company has maintained that the understaffing did not result in an increase of violence or any security problems at the prison.
"We are working day in and day out in the facility to make sure what happened never happens again," Owen said in an email to The Associated Press. "If a post cannot be filled there is a process to document what steps were taken to fill it and, if it couldn't be filled, what was done to address the impact of the vacancy."
CCA officials didn't rule out a possible return to Idaho. The letter said CCA "looks forward to the opportunity to serve the department in the future."