Fiorentina believed they had an agreement in place with Chelsea to extend Salah's loan for another season and subsequently made a complaint to Fifa, alleging a breach of contract.
Salah's party argued that the player's consent was needed before an extension to the Fiorentina loan could be agreed. Fifa threw out the complaint in May 2016 and, 13 months on, Cas has come to the same conclusion.
A Cas statement read: “Cas has dismissed the appeal and confirmed the decision issued by the Fifa dispute resolution chamber on May 26, 2016 (Fifa DRC) in which Fiorentina's claim for compensation of €32 million was rejected.
“The Cas panel found that the player did not breach the employment agreement by returning to Chelsea FC after June 30, 2015 and that Chelsea FC did not induce the player to terminate the employment agreement without just cause.
“Accordingly, it dismissed the appeal and confirmed the Fifa DRC decision.”
Ramy Abbas, Salah's agent, hinted at a verdict in favour of his client on Thursday by tweeting: “How do you say 'clowns' in Italian? And how do you say purple?”
Salah joined Liverpool from Roma for €39m (£34.3m) last week, having scored 19 goals in 41 appearances for the Serie A club last season.
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