When you order a new iPhone at the online Apple Store, as you know, you will be provided with the option to trade in your current iPhone. That process should ask you a few simple questions about the condition of your phone, and provide you with an estimated trade-in value based on your answers. The actual trade-in value will be determined by a third-party that Apple uses to perform the actual review of the phone. At this point, that third-party will either agree with your assessment or not. If they don't, then they will provide you with both a reduced trade-in value and give you to the option to accept it or have the phone shipped back to you.
If this is the process you are using, then you will not have the option to reduce the new phone's cost at this juncture. Instead, you will be asked if you want that amount provisioned to an Apple Store Gift Card, or possibly a number of other choices.
Ref: Apple Trade In - Apple