There's usually two types of contacting former employers when you apply for a new job. There's the contact information/supervisor information from all your jobs and the professional reference.
I wouldn't put them as a professional reference. Your professional references should be saying good things, and you don't want to worry they won't.
If there's something about contacting former employers, you can check no because you are still working there and you don't want them to know you are looking for a different job. I don't think, at least at my old job, they can ask those types of contacts anything more than verifying what you put on your resume/application.