Is he concerned about himself? Does he perceive himself as different? Does he need reasonable adjustments at school, college, Uni or at work to help him do what his peers do?
Does he have deficits in the Triad of Impairments and/or any sensory issues?
If so, then you can suggest he goes for a diagnosis, NHS waiting times vary, often up to 2 years isn't unusual.
He can go privately but often that also needs a GP referral so it's the same first steps and if he needs the dx for an EHCP or reasonable adjustments, it's more likely to be accepted if the team who would offer the dx were "accredited" by the NHS.
He needs to see his GP with a convincing set of details showing why he thinks he may be on the spectrum. The AQ online test could be an indicator, plus any reasons he has for wanting a dx. Also any reports done during childhood like OT, SLT, Ed Psych, Paed.
If he gets a referral, the second step is to be interviewed by a Gatekeeper who has to be satisfied that the person asking for the assessment is not in need of MH support.
It's a very popular question on here, have a look at this recent thread.
www.mumsnet.com/Talk/am_i_being_unreasonable/3428517--to-ask-how-you-go-about-getting-a-diagnosis-as-an-adult-with-Asperger?pg=1