The paper cites a Svenska Dagbladet journalist's blog, which says that the young man died in attacks against the regime in January.
The man, born in 1990 to a Finnish mother and Sudanese father, was fighting alongside Islamist militant rebels known as al-Nusra.
Chief Inspector Tuomas Portaankorva of Finland’s Security Intelligence Service (Supo) said he was aware of the case but refused to comment on it. According to Portaankorva, dozens of people with links to Finland have become involved in Syria's civil war.
"People go there for different reasons. For some, it’s humanitarian work, for others it's an adventure. Some go to join armed combat without much thought to the side they're on," he told Helsingin Sanomat on Monday.