The suspect did not specify a limit, he was just interested in getting a credit card. But if the victim would have been approved under normal circumstances, he would have gotten a $10,000.00 credit limit based on the credit report, salary and underwriting criteria.
IMHO, you're best off using the $10,000 figure as the total of the attempted transaction, regardless of whether it was specifically requested by the fraudster. With that being said, it sounds like you do not have an identified suspect and thus would not be required to file due to the dollar amount being under the $25k "no suspect" threshold.
In terms of voluntarily filing or not, I'd base the decision off how much useful data you anticipate you can provide to law enforcement. Even without substantial identifying information, if the Bank received a good amount of other information that could LE to a suspect than go ahead and file. For example, if the application was received on a mobile device and the bank has the phone number, carrier id, device info, and geo-location data; that could be extremely helpful. Conversely, if you received limited information, it might not be all that useful of a SAR.