Walker's current deal expires at the end of the season and he explored a transfer to Bayern Munich over the summer before deciding to stay at City.
He admitted recently that the length of contract on offer was the main factor in picking City and is set to sign a new deal until 2026.
However, there has been no movement on that new deal being announced and Walker was asked on Saturday if he wants to sign a new contract at City.
Walker had just scored his first international goal for England on his 77th cap and was discussing his City situation after the Euro 2024 qualifying draw with Ukraine.
"I have an obligation to fulfil my contract," Walker told Sky Sports.
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