The Dutch club are still insistent they have a pre-contract agreement with the striker, a claim which is disputed by Alves.
The 27-year-old was sold by Heerenveen to Boro for an undisclosed fee on transfer deadline day but AZ chairman Dirk Scheringa will ask FIFA to investigate.
He told De Telegraaf: "He really has a chance of getting banned from playing for the rest of the season.
"We have a water-tight contract with him."
The Dutch FA (KVNB), who signed off the transfer to Boro on Thursday, have already ruled that the agreement between the player and AZ is invalid because the club have not met certain conditions.