The Dutch Football Federation ruled last week that the Brazilian effectively has two contracts, and now a meeting has been called to resolve the issue.
Alves wants to be relieved of his commitment to AZ so he can move to England, but Boro cannot launch a full offer until his situation becomes clear.
Southgate revealed he is trying to bring in a new face, but he warned Boro fans signing Alves will not be simple.
"We are doing our best to make the breakthrough but nothing is ever simple," he told The Evening Gazette.
"We want to bring someone in, but I can't say that it will definitely happen.
"We just have to keep working away and see what happens."