Velez argued that City had not abided by Federation Internationale de Football Association rules on worldwide transfers when they signed Garre, then 16, and that the world governing body's regulations only allow players under the age of 18 to move between clubs in different countries if both are in the European Union.
However, City argued that, because Garre holds an Italian passport, he was free to leave Argentina after his 16th birthday and were initially supported by Federation Internationale de Football Association before Velez took the case to the Court of Arbitration for Sport (CAS).
If City lose the case, they could be hit with a two-window transfer ban that would not allow them to sign players until January 2019.
Garre has also been active in the UEFA Youth League, scoring home and away against Napoli in the competition's group stage, and played for City's Under-23 team in the EFL Trophy earlier this season, again scoring in the group stage, this time against Rotherham.
CAS has not released its formal decision, but is expected to find the case in City's favour.
That case has been running since July, with a court case heard nine months ago.
"Man City argued that there is an exception in the Federation Internationale de Football Association rules - But the Federation Internationale de Football Association rule does not say that, it says he can move only within the European Union, between EU clubs".
In May 2017, the Premier League fined City £300,000 and banned them from signing academy players for two years after they were found to have approached the family of two young players who were registered with other clubs.
And BBC Sport understands that Cas has now upheld that verdict. City insist they acted within the rules.
That said, they would have the right to a technical appeal that could further delay the process and allow Guardiola to stockpile players this summer. Barcelona, Real Madrid and Atletico Madrid have all been subjected to transfer bans in recent years after being found guilty of breaching rules concerning the signing of worldwide players under 18.
The ban was for two years, although the second year, set to begin on June 30, 2018, will be suspended for three years.