The 35-year-old Algerian national was shot by a Belgium 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-old hunt for suspects linked to the November 13 Paris terror attacks.
According to British TV channel, Sky News, the man listed Sweden as his country of residence before joining the militant group in Syria.
Swedish Radio News reports that 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 offenses from 2011 up to 2013.
The Swedish Security Service Säpo would not confirm whether the victim in Brussels was the same man who lived in Stockholm.
"The information we may have on the matter, we communicate to the Belgian authorities. We leave it to them to establish the identity of the deceased," Simon Bynert, of Säpo's press service, told Swedish Radio News.
In 2012, Swedish Radio News writes, the man was sentenced to one month in prison for stealing a pair of designer jeans from a store in Södermalm, a southern island of Stockholm.
A year later, police accused him of stealing a wallet from someone at a restaurant inside an Ikea store in Stockholm. When police detained him, they found him carrying a folding knife.
The 35-year-old was convicted of weapons crimes and the prosecutor in the case sought to have him deported from Sweden, though the court rejected the request.
Belgian police also found an Islamic State flag next to the man's body as well as an assault rifle and ammunition. During the operation, four policemen were injured and two others arrested though later released. Two suspects escaped police and remained at-large on Friday.