Walker was injured in the team's 4-1 win over Club Brugge in the Champions League group stages.
He limped off during the second half of the game, and is now facing a race against time to get fit for the derby.
According to the Daily Mail, City's medical team will give Walker every chance to prove his fitness.
However, it is touch and go whether he will feature against United, or be given the international break to recover from an ankle problem.
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