The 19-year-old son of former Stoke player Rory Delap is looking to play regular football following an ankle injury that ruled him out of large parts of last season.
His first-team prospects are slim at City, who signed Erling Haaland and Julian Alvarez this summer.
The loan deal will not include an option for Stoke to buy him.
The England Under-19s international marked his senior debut for Manchester City with a goal against Bournemouth in the Carabao Cup in 2020.
He has gone on to make a further five first-team appearances – all as a substitute.
Rory Delap was a crowd favourite during his seven years as a Stoke player and is now first-team coach at the club.