Phil Spencer spoke briefly about a possible Banjo-Kazooie sequel during an interview with Windows Central. 

You’ve seen from our history that we haven’t touched every franchise that people would love us to touch — Banjo fans, I hear you. But it is true that, when we find the right team, and the right opportunity, I love going back to revisit stories and characters that we’ve seen previously.

The right team to make Banjo-Kazooie 3 is Playtonic Games. The right publishers to oversee the project to make sure it’s as good as it should be are Nintendo and Microsoft. One is the IP-holder, the other is the publisher of the first two Banjo-Kazooie titles on the Nintendo 64 who knows a thing or two about making 3D platformers. Microsoft and Nintendo have been working well together the last few years and I’m sure could make this work as well. Microsoft has the IP, Nintendo has the know-how and experience, while the developers at Playtonic are the original creators and developers of the Nintendo 64 Banjo games when they were at Rare. I don’t see how a new Banjo platformer that fans would be happy with could happen any other way.

Unless they opt to make something that’s not a platformer like Rare did with Banjo-Kazooie: Nuts & Bolts on Xbox 360 – but that’s not what fans want. They want Banjo-Threeie.