It’s best to communicate this possibility upfront. In the Mentee Vision Casting meeting if you have one, or in the invite emails you send out.

Your invites have already communicated that you view these men as potential leaders worthy of investing in and mentoring, so if you have more men than spots, let them know the reality, and communicate that the answer (in most cases) isn’t “no,” but “not now.” If they’re still interested, there could be a future opportunity.