Velez complained that City broke rules in signing the young forward, but Federation Internationale de Football Association upheld City's argument that he was free to join them after his 16th birthday, because the youngster has an Italian passport and players in Europe are free to move when they turn 16 if they do not sign a professional contract.
Velez, who have the right to appeal, had claimed that City approached Garre when was 15 and then broke transfer rules by signing him shortly after his 16th birthday.
Velez took their case to CAS after Federation Internationale de Football Association ruled in City's favour, but the South American outfit have seen their claim dismissed.
Were Pep Guardiola not able to invest further in his squad for a whole season it would be a major blow to their hopes of retaining the Premier League title and winning the Champions League for the first time in their history.
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City are very much of the opinion that they did nothing wrong in this case although if they are found guilty they are likely to be slapped with a two-window transfer ban.
City chairman Khaldoon Al-Mubarak was anxious the club would be handed a 24-month ban from making new signings.
City were facing the prospect of being banned from registering new players for two transfer windows, after similar punishments were given to Atletico Madrid and Barcelona. City argued that Garre held an Italian passport and was entitled to move after his 16th birthday.
However, sources have told ESPN FC that City have been given an indication they have been cleared of any wrongdoing, with the decision expected to be announced this week.