An approximate number is fine if you don't know the exact amount.
If you have multiple private loan lenders, please list the name of each. If you are behind on payments, please list the name of any collection agencies on the account (if applicable). Your lender may be different than your loan servicer (for example, most National Collegiate Trust private loans are serviced by AES until they default).
Lenders will only settle when loans are in default or seriously behind. If you're current and considering a "strategic default", first check out my article about the pros and cons of that strategy here: https://www.mycreditcounselor.net/should-i-strategically-default-to-settle-private-student-loans/
If you aren't sure, an approximate date is fine.