State prosecutor Eric Van Der Sypt said his office had received information about possible bomb alerts and had opened an investigation, but declined to provide details. He said the bomb squad had not been called to the airport.
An airport police spokeswoman said no bomb alerts were in place and that there was no problem at the airport.
VRT said both planes, one of which was flying from Oslo, landed safely.
A reporter at Belgian broadcaster Woestijnvis/Proximus TV, Bart Raes, tweeted that he was on the flight from Oslo and that the pilot had received the bomb threat 20 minutes before the plane was due to land.
Raes said that passengers were informed of the threat and had to wait 10 minutes before being allowed to leave the plane after it landed.
Belgian media said some other planes had been diverted to other airports.
Last March, Islamist bombers killed 32 people in suicide attacks at Brussels airport and a metro station. Many of those who carried out last November's attacks in Paris, which killed 130 people, were based in Belgium.
