Doyle is currently on a season-long loan with HSV and has already struck a first goal for the German outfit.
Hamburger Abendblatt says such has been his impact that HSV officials are already considering the idea of extending his loan into a second season.
Doyle is yet to start for HSV, but has impressed coaching staff with his effort and attitude.
This is marking the 20 year-old's first loan move away from City.
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