The way we deal with my almost-three year old when he interrupts is to remind him the polite way to ask for our attention, every time. "Mommy and daddy are talking right now; if you want to talk to us, wait for a pause in the conversation and then say 'Mommy, can I talk now?" Then we confirm that he understands, and go back to talking. What I think is important about this approach is that we give him the right way to handle the general problem of ("I want Mommy to talk to me").
We don't ignore him when he does it, for a similar reason to why we don't ignore him when he's hitting us; the interruption is a behavior we want to correct. However, we don't allow his interruption to keep us from talking, either; we always go back to finishing our conversation (perhaps abbreviated).
It is likely a sign of needing attention if it's happening regularly. We try to acknowledge that when we correct him; we often start with "We know you need our attention sometimes, but it's not okay to interrupt us while we're talking. We sometimes have to talk to each other, too."
This largely has worked; he usually stops after one interruption now. Some of this is probably a feature of how much attention he's getting; when we do talk, we make a conscious effort to involve him most of the time. Some of the improvement, though, has come with his ability to play by himself and talk to himself (verbalizing play). As that improved, he needed to interrupt us less.