Kentucky's positivity rate fell slightly from 3.32% on Saturday to 3.28% on Sunday, according to data from the state.
Beshear later said it was too early to determine if the sites will be able to open Friday.
As of Sunday, 1,709 Kentuckians were hospitalized with COVID-19, and 407 were being treated for the virus in intensive care units.
As of Friday, 1,714 Kentuckians were hospitalized with COVID-19, 390 were being treated for the virus in intensive care units and 216 virus patients were on ventilators, according to the governor's office.
As of Friday, 1,358 Kentuckians were hospitalized statewide with COVID-19, 307 patients were being treated in intensive care units, according to the governor's office.
As of Wednesday, 1,066 Kentuckians were hospitalized with COVID-19, and 286 were being treated in intensive care units.
Counties such as Jefferson, Bullitt, Hardin, Henry, LaRue, Nelson and Shelby were among the 68 marked as "red zones," according to an updated incidence rate map provided by the state.
Starting Monday, the state will begin to calculate the state's positivity rate based off COVID-19 PCR tests that have been sent electronically.
Gov. Andy Beshear said the criteria for commutation will remain the same as the state's first round of commutation, which officials said saw 1,200 inmates released.