The 21-year-old made 27 appearances for the Potters last season but could not stop the club from being relegated from the Premier League.
According to a report from Egyptian sports website KingFut, Sobhi is desperate to stay in the English top flight and has agreed a deal to join Huddersfield.
Sobhi played just over an hour of Egypt's 0-0 draw with Colombia in Italy on Saturday and was then allowed to make a brief return to England.
The Egypt FA confirmed: "Ramadan Sobhi is undergoing a medical screening to move to Huddersfield Town and will return [to Italy] this afternoon."
Sobhi joined Stoke from Egyptian champions Al Ahly for about £5m in 2016.