The Swede, who is thought to be in his 30s and who had been living in Örebro, is understood to be one of a group of three people from the area known to have travelled to the Middle East to join the radical Islamist group, also known as Isis and IS.
According to Mahdi Warsama, chairman of the African Horn Cultural Centre, the man's relatives have received information confirming his death.
Sweden's biggest news agency, TT, reported in June that the trio – two men and a woman – had made multiple attempts to travel to the war-torn region
“I got the information from the parents, they are very worried,” said Warsama at the time. He also told TT that he had personally tried to help stop the youths from becoming jihadists.
Sweden's Foreign Ministry said on Thursday that it was unable to confirm the man's death.
“The current conflict makes it almost impossible for us to get confirmation from Syrian authorities, particularly in the cases of people who have taken part in hostilities,” Johan Tegel, a press spokesperson, told TT.
Sweden's Security Service, Säpo, does not comment on individuals who are suspected of having been killed in fighting.
But the agency has previously said that up to 150 Swedish residents are known to have spent time in Syria or Iraq fighting for Isis or other extremist groups, with intelligence suggesting that at least 40 have died in the process.
Sweden is considering drafting new legislation that would ban its nationals from fighting in armed conflicts for armed extremist groups such as the Islamic State (Isis), the government announced in June.
The proposed ban would prohibit combat for terrorist organisations listed as such by the United Nations or European Union.