The CSA has received close to 90-100 inquiries, president Victor Montagliani says.
"It's getting hotter and hotter, as they say," he said.
The list has been narrowed down, but new calls keep coming.
Montagliani emphasized the most important thing is getting the right candidate rather than meeting a deadline.
The national men's team has been without a coach since Stephen Hart resigned last October following an 8-1 World Cup qualifying defeat in Honduras. Colin Miller served as interim coach for friendlies earlier this year.