S.T.
This is a very annoying and very common problem. I always joke that if I want my kids to talk to me all I have to do is pick up the phone. : )
My kids are now 5.5 and 8.5. When they need to talk with me and I'm in the middle of a conversation they are required to put their hand on my hip. That's a non-verbal cue to me that they need to talk with me. I usually put my hand over theirs to acknowledge their respectful request. Then, when there is an opportunity to break my conversation I praise them and allow them to talk.
This is not perfect because it doesn't address when they are just so excited or anxious that they blurt things out. But, for the most part, it works like a gem and interruptions are much more pleasant and respectful.
Good luck!