I agree with JaggedFrost. Will he use a diagnosis to improve his life or resent your interference? Asperger's seems to run through our whole family. Some in our family feel threatened when faced with the "label" of a diagnosis; they get angry & insulted. Some feel discouraged or hopeless. Others see it as an indicator pointing them in the right direction to find the kind of help they need.
For my resistant family members, I just send them updates of our Aspie boys, symptoms & nutritional things that work & let the family decide for themselves if any of it would be helpful for them.
I sometimes send books or articles which help explain our boys difficulties, in hopes that they will also see their own similarities.
Take it slow and easy & don't push.Many people are more persuaded when they believe they "discovered it for themselves".