Kip Hallman, CEO of Correctional Medical Group Companies, confirmed his company was recommended by a county committee to take over the contract, which is set to expire at the end of June.
Next month the recommendation is scheduled to go before the board of supervisors, which has final say over awarding the contract.
While the amount of the contract has yet to be finalized, Corizon's 8-year contract was worth $250 million.
Correctional Medical Group Companies is the parent company of California Forensic Medical Group, which provides health care for correctional facilities in 27 counties in the state.
The company is facing a class-action lawsuit in Monterey County over medical and mental health care and has been sued by inmates across California for substandard care.
Civil rights attorneys and inmate advocates familiar with the company said it has similar shortcomings when it comes to screening inmates for mental health and substance abuse issues.
"Corizon was pretty bad, so one would hope that another company would be better. It's just that the statistics for CFMG around the state are pretty bad as well," said Michael Haddad, a civil rights attorney who has filed numerous lawsuits against the company.
Alex Friedmann, managing editor for Prison Legal News, said the move was like "getting rid of McDonald's for Burger King."
Friedmann said though there also are flaws with inmate health care provided by public entities, he believes that health care provided by private companies is damaged by the need to make a profit.
Hallman said he disagreed with such criticisms, but declined to elaborate.
He said that one of the company's strengths was its commitment to staffing.
"We have a much lower turnover rate than other companies," Hallman said.
Between 2012 and 2015, the company's turnover rate for clinical staff was below 9 percent, according to Hallman.
In recent years, Corizon had come under fire for spotty care and inadequate staffing at Santa Rita Jail in Dublin and Glenn B. Dyer Detention Facility in Oakland that together house about 2,850 prisoners.
The company, along with the county, settled a landmark lawsuit last year over an in-custody death.
The children of Martin Harrison filed suit alleging their father wouldn't have died during a confrontation with prison guards if nurses had realized he was suffering from alcohol withdrawal during his intake screening.
In addition to an $8.3 million settlement, Corizon agreed to have only registered nurses -- not licensed vocational nurses -- conduct assessment screenings starting in January 2016.
Corizon also was sharply criticized by nurses working at the jail after it fired 49 licensed vocational nurses in January and 16 more in February.
Some remaining employees said they were forced to work double shifts and that the skeleton crew of clinicians was so overworked that patient care was compromised.
Hallman said his company intends to comply with all requirements of that settlement.
Sal Rosselli, president of the National Union of Healthcare Workers, said he was cautiously optimistic that staffing would improve under the new operator.
"We've talked about a common goal of increasing the nursing hours and staff," he said.
Corizon said it intends to appeal the recommendation.
"We're hopeful the county will ultimately decide to continue working with us," said Harold Orr, clinical director of Corizon Health California. "It'd be our privilege to continue serving some of the community's most vulnerable people."