City reacted angrily when they were referred to the adjudicatory chamber of UEFA’s club financial control body by its investigatory chamber in May.
The club said it would appeal to CAS, but the sports court dismissed their initial appeal, saying on Friday that City had not “exhausted the legal remedies available to it prior to the appeal”.
It means City have failed in their attempt to stop UEFA from investigating the allegations they supplied false financial information, with CAS saying their appeal was “inadmissable”.
The investigatory chamber had also recommended that City be sanctioned by UEFA.
The investigation into City is based on leaked emails published last year by German magazine Der Spiegel as part of “Football Leaks”.
Possible punishments include a suspension from the Champions League, a transfer ban or a fine.
