Thanks Jon and Chronanon for your suggestions. I can see both perspectives, but am leaning towards Chronanon's idea of requesting a meeting to explore fit before applying for the position. If there isn't a good fit, I at least let the director know of my interest in the program, and leave the door open for us to collaborate in other ways.
I would be curious to know what others think. Thanks again for your suggestions
I agree with chronanon, but only if you know this person reasonably well (well enough, for example, to invite him or her out for lunch). I don't mean you have to be friends, but I'd be less likely to contact him or her if I met him or her once for three minutes at a university function two years ago and s/he barely remembers me.
And simplesimon is right, if you're likely to bump into this person through the ordinary course of business, you can use that occasion to express your interest ("Hey, guess what--I'm thinking of applying for that position. What do you think?" or "Can you tell me more about what they're looking for, because I'm trying to decide whether I should apply" or something like that) and see how s/he responds. If you get a blase "that's nice" reaction, you let it go and apply (or not) as if you didn't have the contact (because, essentially, you don't). If the person reacts more favorably, you can take the conversation further and see where it leads.
Good luck, either way.