The airport has not handled passenger flights since two suspected Islamist militants carried out the attacks. Those bombs and a separate one on a metro train in the city killed 35 people in all and wounded scores of others.
The airport, whose departure hall was destroyed in the blasts, has built a temporary check-in zone, conducted tests and had declared itself ready to restart flights.
The federal police, whose officers work in the airport, wants passengers to be checked outside the new departure zone. But the airport authorities say this would mean passengers waiting too long and simply shift the security threat from inside to outside the area.
Airport police say they are ready to strike over the issue.
"We need an agreement with the police unions. There are currently discussions between them and the interior ministry," an airport spokeswoman said, confirming there would be no passenger flights on Friday.
Belgium's national security council, a grouping of senior ministers, police and intelligence chiefs, earlier acknowledged it could simply force police to work at the airport, but that it would be unwise to do so.
"It's important to find the right balance between economic interests and security interests," Defence Minister Steven Vandeput told Belgian television.
Brussels Airlines, Belgium's largest carrier and 45 percent owned by Lufthansa, has estimated the closure of its Brussels hub is costing it 5 million euros per day.
The city's association of hotel operators pointed to the closed airport as one of the main reasons for a more than 50 percent drop in overnight stays up to March 28.
"The outlook is bad but it depends on the complete reopening of the airport," a spokesman for the Brussels Hotel Association said.
Brussels Airport is one of the largest airports in Europe, handling 23.5 million passengers and 489,000 tonnes of freight annually. It links the Belgian capital with 226 destinations worldwide through 77 different airlines.
When it does reopen it is set to run at only 20 percent capacity, with some 800 passengers departing per hour.