Coaching isn't just about helping someone to do something. Almost as often and sometimes even more importantly it's about coaching someone away from something.
Most often I've had to coach people away from wanting to get into Management. Now to be fair it must be stated that in most companies the only way to advance is to move into management. Management is the only path to more money or more responsibility. The only problem is many people are not necessarily interested or talented in managing other people. Frankly, bad managers do a tremendous amount of damage to a company both in terms of low morale and lost hours of productivity. Think back to a really bad boss you've had - I'm sure you can remember the stories, the scars, with painful preciseness. Think about how much energy you spent dealing with, stressing over, venting about and working around this bad manager. $$$ right out the door and precious, productive time wasted on your part.
There's a famous saying that holds true: "People join companies but they leave managers."
As a coach working with a managerial "candidate" helping someone move away from an ill-fitting role will not just help that individual but the entire organization and anyone unlucky enough to have to report to this person in the future.
Leading people is a skill - a very specialized skill - and like any other skill some individuals are born naturals, others acquire the skill through hard work and practice and others simply aren't that interested or can't "get it".
The key with entering Management is ensuring that a person's motivations are not self-serving. If money or professional political power are the goals this person needs to find other paths. If this person however enjoys watching and helping others grow, shows great empathy for others, communicates well and exhibits strong interpersonal skills then we have someone much more likely to succeed. How do I go about and figure this all out?
The core of any coaching conversations is: Questions!
Just asking questions isn't sufficient of course. It's asking the right questions and allowing the conversation to meander until you hit the reasons behind the reasons. One of my favorite techniques is asking a person to imagine they already are in the position they desire and then having them describe what this looks and feels like to them. I then I listen very, very intently. If the picture they paint revolves around having a new office or secretary or "finally" getting people to listen to them a red alert starts flashing in my mind. On the other hand if this imagined environment includes strategizing, leading teams and enjoying their own future coaching sessions then I'm glad to pull them further in that direction.
Now I've been very lucky to have worked at 2 companies who were "enlightened". They provided a career path on two tracks: one managerial and one non-managerial. Obviously a conversation around whether entering management is the right next step is far easier in this environment because you can provide an established alternative. But even in the absence of a parallel track these kinds of conversations are critical. Perhaps you and your mentee can help create a parallel, non-managerial track at your company. Or once you understand the person's underlying motivations you can find alternatives for those specifically. Perhaps "management = recognition" to that individual. There's plenty of ways to gain recognition without getting into management. As an example that person could go author and present white papers at conferences and possibly gain even more recognition than getting an internally-focused, corporate promotion.
I'll end by saying that figuring out people's motivations and coming up with creative ways together to satisfy those motivations when operating under constraints is one of the most fun things for me personally in a mentoring relationship. We all have a part to play in this world to make it successful. Some are managers and some are not but all are valued and indispensable.