The man, a 35-year-old Algerian national, was shot by a Belgian police sniper after he holed himself up in an apartment in the Forest neighborhood of Brussels.
Authorities zeroed in on the man during their four-month hunt for suspects linked to the November 13 Paris terror attacks.
DN reports that Belgium's public TV service, RTBF, said the apartment was rented by one of the brothers who are now also suspected of Tuesday's blasts.
Two months prior to the attacks in Paris, the 35-year-old Algerian was also stopped during a security check between Austria and Hungary with the Moroccan national who is considered the mastermind behind the attacks.
The second brother, also a suspect in yesterday's blasts, is believed to also have been in the vehicle.
Last week, Swedish Radio News reported that a man with the same name, birthday and citizenship was registered with the Swedish Tax Agency as living in the Stockholm area. He has also been arrested for various minor offences between 2011 and 2013.
Tuesday's DN reported that the man came to Sweden in 2010 and married a Swedish woman. He was granted residence one year later, and subsequently lived in a municipality north of Stockholm.
In 2014, he travelled to Syria to join so-called Islamic State. According to information originally reported by Sky News, the man had indicated he was willing to be a suicide bomber.
Sweden's security service, Säpo, would not comment to DN about any connections between the attacks in Brussels and Sweden.