According to the newspaper, the man, who was born in Somalia but had lived in Norway for several years, was killed during the conflict over the last few days.
Martin Bernsen of the Norwegian Police Security Service refused to confirm Dagbladet's information, which seems to have come out in response to the arrest yesterday of three men on suspicion of involvement in jihadi groups I'm Syria.
"We have no comments on Dagbladet's information," said Martin Bernsen, the press officer for the Norwegian Police Security Service.
At least seven Norwegian citizens have been killed so far in Syria, all of whom were reportedly involved Islamist group Islamic State of Iraq and the Levant (ISIL).
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Norway's security services on Monday arrested a 29-year-old Somali, and two Kosovans, one 24 and the other 27.