Contracts finalized this week total $76 million for the first month, though much of that is likely to be covered by the federal government.
Judges say no one in jail is currently being held on minor, non-violent charges alone.
First 120 beds will be ready this weekend, Edwards says.
Board chairman Melvin Rodrigue said a decision could come down from the state "by the end of the day" on Wednesday.
Layoffs are related to advertising losses due to the coronavirus pandemic. Executives say they hope the cuts are temporary.
Order goes into effect at 5 p.m. Monday.
Tests for the public begin Sunday.
City official says the centers should open to the public eventually, but the timeline for that is unclear.
Despite assurances from Mayor Cantrell that quarantined employees will get "civil leave" pay, three employees told The Lens they are currently on unpaid leave.
Defense attorneys say city's jail is a dangerous environment during an outbreak.