The 23-year-old, who was recently on trial with the Championship club, is believed to be keen on a move to England.
It had been suggested that his club were unprepared to sanction a move, but sporting director Jan Girgo has now admitted that Sow is now likely to depart the Swedish outfit.
Girgo told Fotbolldirekt.se: "It looks like Osman will leave us. We would like to keep him, but I can understand that it is difficult to reject a lucrative offer from there.
"There is still a chance, but it is not likely that he will stay with us."
Sow joined Syrianska in May 2013.