Delta has 90,000 employees. Earlier this week, the company said a Delta ground handler in Detroit had died from the coronavirus.
The airline said it can confirm that some employees have tested positive, but is not confirming specific numbers.
Delta said if a crew member is confirmed to have COVID-19, it works with the Centers for Disease Control and Prevention on steps to notify employees and customers who might have been in close contact with the crew member.
If an employee has COVID-19 symptoms, Delta said it will contact employees who came in close contact with the person starting at 48 hours before the symptoms began, and may notify the employee of a need to self-quarantine.
The Air Line Pilots Association has called for the Federal Aviation Administration to require airlines to comply with Centers for Disease Control and Prevention guidelines for notifying employees after a positive COVID-19 test.
"ALPA has learned that this life-saving notification process is not being uniformly obeyed," wrote Air Line Pilots Association, International president Joe DePete in a letter to FAA Administrator Steve Dickson.
On Friday, Delta CEO Ed Bastian wrote in a memo to employees that those who are in higher-risk categories and are particularly vulnerable "should not be at work — we have options that help protect you financially to keep you at home and healthy."
The company also invited employees to volunteer for unpaid leave while retaining their benefits and better travel privileges.
Last month, the pilots union at Delta reached a deal with the company to offer pilots time off at reduced pay.
The Association of Flight Attendants, a union that represents flight attendants at other airlines but not at Delta, said Thursday that about 150 flight attendants from multiple airlines self-reported that they had tested positive.
Several hundred other flight attendants are self-quarantining because they have symptoms or came into contact with someone who tested positive, according to the union.
Delta’s flight attendants, airport customer service employees, baggage handlers and mechanics are not unionized.