The RTBF broadcaster said the pair were known to police. It is believed at least one was among three suspects seen in a CCTV image at Zaventem airport.
Twin explosions at the airport and another at a metro station on Tuesday left about 34 dead and 250 wounded.
Belgium is observing three days of national mourning.
So-called Islamic State (IS) has said it was behind the attacks and warned that more would follow.
A minute's silence for the victims will be held at midday (11:00 GMT).
RTBF said the brothers were known to police and had criminal records.
The broadcaster said that Khalid el-Bakraoui had used a false name to rent the flat in the Forest area of the Belgian capital where police killed a gunman in a shootout last week.
It was during that raid that police found a fingerprint of Salah Abdeslam, the main suspect in the Paris terror attacks of 13 November.
He was arrested in a raid in Brussels last Friday and is due to appear before a pre-trial court on Wednesday.
It is not known if both of the brothers are in the CCTV image handed out by police of the three men at the airport.
Some Belgian media say that one of the brothers may have carried out the metro attack.
Belgian newspaper La Derniere Heure said Khalid el-Bakraoui was being sought for terrorist activities while Ibrahim was reportedly on the run after a sentence for other criminal activity.
La Derniere Heure also said that the man wearing the hat in the airport CCTV image is Najim Laachraoui.
Laachraoui was named earlier in the week by police as a wanted accomplice of Abdeslam.
The three men were seen pushing trolleys carrying suspected bombs at Zaventem airport just before the blasts at a check-in hall.
Two of the men were wearing black gloves on their left hand, possibly hiding a suicide detonation device.
They were believed to have died in the attack. The third man was wearing no glove.
The airport explosions happened in quick succession shortly after 08:00 local time (07:00 GMT), killing about 14 people.
A third bomb was found and destroyed in a controlled detonation.
About an hour later another explosion ripped through a train at the Maelbeek metro station in the Belgian capital, killing about 20 people.
Belgian Prime Minister Charles Michel said Tuesday was "a day of tragedy, a black day".
The country has raised its terrorism alert to the highest level.