Relatives of the 23-year-old man confirmed that the mother of the deceased had over the weekend been informed of her son’s death, according to the news report.
The mother was told that his son had died from cardiac arrest.
The man is said to have secretly left for Syria in December 2012 without his family’s knowledge.
He was of Somali background and had moved to Finland when he was just two years old.
If the death is confirmed, he will be third Finnish citizen to have died in Syria’s fighting.
The Finnish intelligence agency, Supo, however, did not confirm the death to the newspaper.
Earlier on March 5, the annual report of Supo said the security agency has identified more than 30 people who have travelled to Syria from the country.
About one in every two is thought to have left to fight in Syria. At least two Finnish citizens died in the fighting in Syria, Supo sources said.
Yle reported that individuals from different ethnic groups including Finnish converts to Islam have travelled to Syria from Finland.