depends how close it is, but I agree that once your into Monday your effectively in this week which the comming Saturday is part of therefore the upcomming Saturday is this Saturday (in reference to this week) and next Saturday the following week.
I always confuse people with this! It's Friday today and I class 'next' saturday as not tomorrow but the Saturday after. (*This* saturday is tomorrow) But technically, the 'next' saturday is tomorrow as it is indeed the *next* Saturday. I don't know why I've always said this - it must be a dialect thing!