[HuShifang]

Generally speaking, auditing is allowed solely at the professor's discretion (though as you surmise, I don't think institutions are fans of the concept). So, I'd definitely approach the professor directly. BUT I do think you might have a hard time winning them over -- usually it's only people who are registered students or faculty/staff at the institution that are allowed to audit there (and plenty of faculty will say no, esp. if the class isn't a large lecture). Sometimes alumni are allowed to audit, but there may be security concerns, etc. about letting total outsiders into the classroom. (And as test grading takes time, that may also be a no-go.)

My advice would be to 1) consider MOOCs or MIT OCW, and 2) attend lectures and events open to the public at the institution. The latter may be interesting in themselves, and would be a way for you to get to know the scholarly community a bit better (so you're not just a random person asking for consideration).