You are allowed to do reference checks at whatever point in the selection process it makes sense to do reference checks. There is no OFCCP-related rule that dictates when reference checks must occur. OFCCP may be concerned if it finds that you are doing reference checks at a different stage in the selection process for members of a certain classification (i.e. you do reference checks for African Americans earlier than reference checks for whites), but so long as you do the reference check in a logical and uniform uniform way, OFCCP would suggest you have wide latitude on when and how to do the reference check.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.