City signed Ortega, 31, from Arminia Bielefeld in the summer of 2022.
The German goalkeeper has managed to play 23 competitive matches since then and kept a clean sheet eleven times.
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The 31-year-old's current contract with the English giants runs until 2025.
City would like to extend Ortega's stay, but Sky Deutschland says negotiations have stalled.
The parties have not managed to agree on salary. Ortega wants to be number one again and a move this summer is possible.