The Potters will pay a fee of around £2.5m for the winger and will loan the youngster out to another European club as he is ineligible to play in the UK due to work permit regulations.
Sobhi has played for his country six times in the past 12 months, which is not enough for the Egyptian to be granted a work permit.
The 19-year-old has played 67 times for his club Al Ahly, scoring 14 goals. He also has one goal in his six international appearances.
Will Sobhi come good for Stoke?