The Australian under-20 International made his first appearence of the season as a half-time substitute in Saturday's 3-0 defeat at Rochdale, but the midfielder has now decided to return back to his homeland after just seven months spent as a professional.
"He wants to go back to Australia and is homesick," Thordarson told the Nottingham Evening Post.
"He has been in that state of mind for a while and that explains others things as well."
Zadkovich's imminent departure - as well as that of Shane McFaul, who was released recently - may free up room for Thordarson to bring in another player at Meadow Lane, though the Notts manager was realistic about his prospects when he was asked the question today.
"Even if I put together what I will have saved on both of those two players, it would not be able to bring in the quality of player I am after," the 50-year-old admitted to the club's website.
Skillful Zadkovich has made nine first-team appearences for the Magpies - including his final match on Saturday at Spotland.
After netting on his debut, the midfielder impressed Notts fans with his industry and tenacity at the back end of last season, though the 19-year-old found his first-team chances serverly limited this campaign.