The 20-year-old broke into the Man City first team in 2024-25, making six appearances under then manager Pep Guardiola.
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Simpson-Pusey was then shipped out on loan to Celtic last summer before being recalled and then sent back out to FC Koln, where he made 11 appearances.
According to journalist Florian Plettenberg, the German club have agreed a €5 million deal to sign the centre back.
FC Koln originally had a €8 million release clause included in the deal but were able to renegotiate it with City.
The youngster has also agreed to a four-year deal with the Bundesliga club.