I'm not even going to get into whether it's appropriate or not; that depends in part on the individual kids involved. What matters here is that if YOU are not fully comfortable with it, then go with your gut and don't do it, no matter what anyone else thinks is the right or wrong age for anything. When your son says, "Please, mom?" just say, "How about this..." And offer them something fun, special and out of the ordinary play date routine -- maybe a nighttime excursion into the back yard with good binoculars to see if they can spot some stars (bring a simple kids' constellation chart, bet you can find them online!). Or a Saturday trip to the DC museum of their choice -- Smithsonian museums are free! Or a drive to someplace like Mount Vernon, which now has a great museum that's very kid-friendly.
They probably both would mostly like to do something that's outside their usual box, and in this case, I think you don't really owe your son a full explanation of any reservations you have about a sleepover; you can say, "I don't think that'll work for us, but how about..." And they'll both have a great time. Take advantage of the fun this area offers and they'll get off the subject. I usually favor talking as honestly with kids as possible but without introducing adult issues they shouldn't have to think about yet. So in this case, I think over-explaining adults' reservations to him at his age could only introduce the idea of "Should I feel weird about having such a good buddy who's a girl?" and you don't want to get that started. It's not weird, it's great. But if you as the parent aren't comfortable with a sleepover, don't do it. Too much else to offer anyway.