Leicester confirmed last week that they had reached an agreement with Freiburg to sign the 22-year-old, who is a 15-time Turkey international.
The transfer window for English clubs closed last Thursday, and there was confusion surrounding the move as neither club has officially confirmed the transfer.
However, according to Turkish Football, the deal will be signed off before the end of the week, with Leicester said to be paying an initial £18.3m for the defender, although the price could eventually reach £20m.
Soyuncu - previously been linked with Arsenal - has made over 50 appearances for Freiburg during the last two seasons.
The Turk has already undergone a medical and agreed terms on a five-year contract at the King Power Stadium, with his work permit due to be approved on Friday.