The 22-year-old has been a key fixture in the Bundesliga side's backline over the last two seasons and remains under contract at the Schwarzwald-Stadion until 2021.
Soyuncu has been widely tipped to complete a move to the King Power Stadium but no announcement was made by the club before Thursday's 5pm deadline.
According to Sky Sports News, however, the deal should have been completed before the window slammed shut, subject to a work permit that the Foxes are confident of obtaining.
The report claims that Soyuncu already has endorsement papers from his football association, but if the work permit application fails, the deal is aborted and Leicester pay nothing.
Last year, Leicester missed the deadline to register Adrien Silva by 14 seconds.