I don't know what the current rules are but in the past if you needed to move the award miles booked on a saver award it cost the same as a standard flight change fee. And usually 12.5K are the base line saver awards for longer distance domestic flights.
Edit: See below from
https://www.aa.com/i18n/aadvantage-program/miles/redeem/award-travel/award-travel.jsp
Changing flight awards
Contact American Airlines Reservations for assistance with changing a flight award ticket.
Changes to the origin or destination or airline
- For MileSAAver awards, origin or destination changes to the itinerary will incur a change fee of $150, even when retaining the same award type
- For awards involving travel on other airlines, origin or destination changes or changes to the airline(s) in the itinerary will incur a change fee of $150, even when retaining the same award type
- For AAnytime awards, origin or destination change fees are waived only when retaining the same award type
- The change fee will be waived for Executive Platinum members using miles from their account
Changes that require a different award type
- Changes to the itinerary which involve different AAdvantage awards than originally ticketed require a reinstatement of the original award ticket, payment of the applicable award reinstatement fee, and a new award ticket issued
- The award reinstatement fee will be waived for Executive Platinum members using miles from their account
Changes to your travel date
- If you change your outbound award travel date to within 21 days of the original booking date, a $75 award processing fee will apply, provided the new date is valid for the original award type claimed
- This award processing fee will be waived for Executive Platinum, Platinum Pro, Platinum and Gold members using miles from their account
Changing mileage upgrade awards
Contact American Airlines Reservations for assistance with changing a mileage upgrade award.
- Tickets upgraded with mileage upgrade awards retain all the original fare rules and restrictions of the original purchased fare
- Changes to the itinerary which do not require a different mileage upgrade award than originally ticketed do not require payment of the award reinstatement fee. Any co-payment amount already paid can be re-applied towards the upgrade co-payment for the new itinerary. Any fare rules, restrictions or fees that apply to the original purchased fare still apply
- Changes to the itinerary which involve different mileage upgrade award(s) than originally ticketed require a reinstatement of the original mileage upgrade award, payment of the applicable award reinstatement charge, forfeiture of any non-refundable co-payment as well as payment of any fees that apply to the original purchased fare
- Reservations service charges paid are non-refundable.
Reinstating flight awards
Contact American Airlines Reservations for assistance with canceling your flight award reservation and requesting mileage reinstatement.
- You can request to have your AAdvantage mileage reinstated for a wholly unused AAdvantage award ticket and if the ticket has not expired. For tickets booked on or after November 1, 2018, you can request to have your AAdvantage mileage reinstated for a wholly unused AAdvantage award ticket if your reservation is canceled prior to departure and if the ticket has not expired.
- The reinstatement charge is $150 per account for the first award ticket. Additional award tickets reinstated to the same account at the same time will have a $25 charge per ticket.
- This fee will be waived for Executive Platinum members using miles from their account.
Reinstating mileage upgrade awards
Contact American Airlines Reservations for assistance with canceling your mileage upgrade award and requesting mileage reinstatement.
- You can request to have your AAdvantage mileage reinstated for a wholly unused mileage upgrade award if the ticket has not expired. For tickets booked on or after November 1, 2018, you can request to have your AAdvantage mileage reinstated for a wholly unused AAdvantage mileage upgrade award if your reservation is canceled prior to departure and if the ticket has not expired.
- Tickets upgraded with mileage upgrade awards retain all the original fare rules and restrictions of the original purchased fare.
- There will be a $150 reinstatement fee per account for the first mileage upgrade award, plus forfeiture of any non-refundable co-payment. Additional mileage upgrade award tickets reinstated to the same account at the same time will have a $25 reinstatement fee per ticket, plus forfeiture of any non-refundable co-payment.
- Cancellations to the original ticket purchased 2 or more days prior to departure will have up to 24 hours from the time it’s ticketed to be eligible for a full ticket refund including the reinstatement of award miles, co-payment amount paid and AAdvantage award processing fee. If you cancel the ticket on aa.com, you must call Reservations to request the reinstatement of award miles and refund of any co-payment or processing fee paid.
- The award reinstatement fee will be waived for Executive Platinum members using miles from their account.