Salah suffered a hamstring injury during victory over Crystal Palace on Saturday.
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While Liverpool are yet to offer an update on the extent of the setback, Hassan told Reuters: "He has suffered a hamstring tear and will require four weeks of treatment."
Salah will leave Liverpool this summer after nine years with the club.
If Hassan's assessment is correct, the Egypt striker will struggle to make the final game of the season against Brentford in the final week of May.