The RTBF broadcaster said Khalid and Brahim el-Bakraoui 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 Zaventem airport and another at the Maelbeek metro station left about 34 dead and 250 wounded.
Belgium is observing three days of national mourning.
ISIS 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.
RTBF said the brothers were known to police and had criminal records.
The broadcaster, quoting a police source, said that Khalid el-Bakraoui, 27, had used a false name to rent the flat in the Forest area of Brussels 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 November 13.
Salah Abdeslam was arrested in a raid in Brussels on March 18 and is due to appear before a pre-trial court on March 23.
Khalid el-Bakraoui is on the Interpol website. It says he is being sought for terrorist activities.
RTBF said Khalid el Bakraoui was jailed for five years in 2011 for car-jacking while his brother Brahim, 30, was sentenced in October 2010 for firing at police.
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.
Meanwhile, Belgian newspaper La Derniere Heure said that the man wearing the hat in the airport CCTV image is Najim Laachraoui.
Najim Laachraoui was named earlier in the week by police as a wanted accomplice of Salah Abdeslam.
Federal prosecutors have not commented on the latest reports but said they would provide more information on March 23.
The three men were seen pushing trolleys carrying suspected bombs at Zaventem airport just before the blasts at a check-in hall.
Two were believed to have died in the attack, while the man in the hat is still being sought.
The airport explosions happened in quick succession shortly after 08:00 local time, 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 Brussels, killing about 20 people.
The first of the victims to be named is Peruvian Adelma Tapia Ruiz, 37.
Adelma Tapia Ruiz had been at Zaventem airport with her Belgian husband and twin four-year-old daughters, who were unharmed, her brother told Peruvian radio.
Belgium has raised its terrorism alert to the highest level.
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