Rush, 64, was admitted to the Countess of Chester hospital last week with breathing difficulties.
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It's since been announced Rush has been suffering with flu.
A Liverpool spokesperson thanked staff at the hospital for "providing the best care possible" and said "everyone at Liverpool wishes him a speedy recovery".
Rush, who also played for Leeds, Newcastle and Wrexham over a 22-year career, won five First Division titles and two European Cups with Liverpool.
