The official police notice said they were seeking to formally identify the man, who is suspected of dumping his case, which contained a bomb, before running from the terminal, and called for information.
A man widely reported to be the third individual in CCTV footage of two suspected suicide bombers at Brussels airport was released on Monday for lack of evidence.
Belgium's federal prosecutor's office said it had freed a man it had named only as Faycal C., adding it had no evidence to justify holding him. He had been charged on Saturday with "terrorist murder".
Belgian media had identified the man as Faycal Cheffou and a source close to the investigation had said officials believed he was the man in the footage.
Earlier on Monday, police had issued an appeal for witnesses, saying they were seeking to identify the man caught on CCTV with two others thought to have blown themselves up. Police say the third man appeared to have left his bomb, which failed to explode, and fled.
The death toll from last Tuesday's bombings at Brussels Airport and a rush-hour metro has risen to 35, the health minister said on Monday.
"Four patients deceased in hospital. Medical teams did all possible. Total victims: 35. Courage to all the families," Maggie De Block said in a tweet.
The figure includes three suspected suicide bombers. More than 300 people have been injured.
Belgium's crisis centre previously said that 28 of the victims had been identified. Of these, 15 died at the airport of whom six were Belgian and nine were foreign nationals.
The 13 victims of the metro blast included 10 Belgians and three foreign nationals.
The foreigners killed in the attacks were British, Chinese, Dutch, French, German, Italian, Swedish and U.S. nationals.
Belgian police seek information on "man in the hat"
Belgian police issued a new appeal on Monday for information about a man caught on CCTV at Brussels airport with two others thought to have blown themselves up in the check-in area last Tuesday.
The man, seen pushing a trolley with a suitcase on it in video footage released along with the appeal, has been dubbed "the man in the hat" and named by Belgian media as Faycal Cheffou, a self-styled freelance journalist.
A source close to the investigation, speaking on condition of anonymity, said a man arrested and charged with actual and attempted terrorist murder, who prosecutors named only as Faycal C, was believed to be Cheffou.
But the source repeated that there had been no official identification, implying police may be having difficulties linking him to the figure captured on CCTV, who was wearing glasses and whose hat was pulled down over his face.
REUTERS