The governor of North Carolina says he's working like crazy with NASCAR and health officials to keep the Coca-Cola 600 Memorial Weekend race on schedule as planned next month ... but without fans in the stands.

Gov. Roy Cooper announced the plan to keep the May 24 race as scheduled ... saying the state has been in contact with NASCAR and the Charlotte Motor Speedway to come up with the safest possible social distancing protocol.

"We believe that unless health conditions go down, we believe we can hold the Coca-Cola 600," Cooper said on Tuesday ... adding NASCAR will make a statement on the decision later this week.

The state of North Carolina has extended the stay-at-home order through May 8 ... but Cooper deemed pro race team shops "essential businesses" to allow them to prepare for the future.