Acceptable to only give references post interview?

So a company contacted me for a phone interview coming up soon, and wants me to fill out the application before the phone interview. In the application is 3 boxes for references. Would it be appropriate to put in one of the boxes "References available post-interview if mutual interest is established"?

I don't want to burn my references and annoy them by constantly asking them to be a reference and informing them a call is coming which may or may not come, so I don't want to provide names and contact details until a company is reasonably interested in hiring me after an interview. Is this fair?

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