The former AZ Alkmaar midfielder, now in his second season with Milan, has been excellent for the Rossonero this season.
The Daily Star say City are monitoring the Holland international and are keen to bring him to England next month.
The city is preparing a £50m offer for Reijnders for the January market.
He would initially serve as cover for ACL casualty Rodri, although it is believed the pair could play in the same midfield in the long term.
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