As a scout myself that has been SPL, I struggled with my assistants at times. Some scouts asked me for an ASPL position, but I felt they were not ready for it. I spoke with these individuals and we came to a conclusion. Unfortunately I did have a rather angry dad call me up demanding to know why his son was not an ASPL. I simply explained to him that his son needed more leadership experience and a willingness to jump headlong into tasks that need to be done without specific directions. I also had all the ASPL' needed. I did offer this scout a several different positions that would put him in a good place to show he is ready to be an ASPL. I would suggest the same thing for this Self-Designated ASM. Offer him a position that will give him an opportunity to show and share his skills. If he can successfully complete this job, than he deserves consideration for an ASM position, but only when one becomes available. Give him the opportunity to be involved. You would not want the scouts to exclude eachother.
I agree with FScouter. Talk to him at the next meeting and learn more about his intentions.
Always remember that the scouts are watching and act appropriately. Assume that they know more than you think about the adult politics, as a scout myself I know we do