But the Brazilian joined Boro for £13m in January after AZ failed to reach a transfer agreement with Heerenveen.
AZ took the case to the Dutch FA but they ruled that Alves could move to the Riverside.
But AZ are not giving up and have taken their case to FIFA. They want the governing body to suspend Alves, 27, if his agents and advisors refuse to pay the compensation.
The case will now be presented to another panel with the hearing set for May 19.
Alkmaar's lawyer Eric Vile said: "We are claiming this money based on FIFA's rules."