Several Swedes have also apparently been admitted to hospital in Turkey.
The Swedes were friends and have been celebrated as "martyrs" on social media since their deaths earlier this week, according to Expressen. The man from Gothenburg was 23 years old.
Sweden's Ministry for Foreign Affairs could not confirm the deaths of the two Swedes. Sweden's National Bureau of Investigation and the Swedish intelligence service (Säpo) both declined to comment on the information.
Säpo has previously said that at least 75 Swedes have travelled to Syria to fight in the civil war there. So far, around 15 Swedes are thought to have died in Syria.