It seems like the FAA doesn't want us talking to the airports directly.
For official airspace authorizations,
no they do not. But trust me, whenever you're operating withing 5 NM of most staffed airfields, the airport managers normally DO want to know you're out there. You are NOT calling for authorization, merely making a responsible notification to them. They will make a note of the information you provide just in case there is an incident or problem. I always make it a point to call to provide a courtesy notification to local airfields if I'm operating within a 5 MI boundary, especially within a transition zone. Many have stopped notifying airports, confusing it with requesting an airspace authorization. If you're not in controlled airspace, they will never know you're there.
Here's a perfect example...
I completed a commercial shoot yesterday, 3 MI from the local airport (G airspace.) I called and spoke the the airport manager about an hour before I was going to start. He took down my information and was very pleasant on the phone. I advised him that I would be starting my operation at 1:45 pm <200' AGL.
At EXACTLY 1:45 pm, a Cessna 172 flew directly over my operating area at what I approximate to be 300'-400'. This was a little TOO coincidental as far as I was concerned. I had just lifted off to start my shoot, but heard the aircraft approaching and dropped down to a low hover as I made visual contact. My VOS was rather shocked to see the plane that low in that location. I honestly was not surprised and immediately had an idea of what happened.
When we were done with the shoot, I drove over to the airport to try and meet with the Manager and drop off a business card. I believe in transparency in business practices, and this was a good opportunity to meet someone face to face at this busy little airport. We had a nice conversation and I explained to him what happened. He knew exactly who the pilot was - had just taken off prior to that time. Without directly saying it, we agreed that the pilot was being 'nosey' over my operating location on his 'very slow altitude climb.' The pilot must have been standing in the terminal building when I called and overheard the conversation (small-town style.) The point of my visit was not to '*****' about what had occurred, but simply verify my thought process through a friendly conversation. Curiosity.
You can come to your own conclusions about this example, but I just wanted to share it as a real world example of what can happen on any given day. This is a big part of the reason I choose transparency and the opportunity to talk to people in the aviation community about UAS. We face a stereotype of ignorant, irresponsible idiots that are crowding the skies and should take every opportunity we can to dismiss that mindset.