While it is possible Rare is creating an entirely new game, nearly everyone expects a remake of one of the aforementioned IPs, with a Banjo sequel the most likely.
If indeed it is a new Banjo, there will be an interesting rivalry brewing. Most of the developers behind the original game are currently working on Yooka-Laylee, a platformer in the exact spirit and concept as B-K, but without the original IP or the big funding of Microsoft. Yooka-Laylee has raised $2 million on Kickstarter in just 48 hours showing that there is certainly a market out there for cartoon duos going on adventures.
Furthermore, Yooka-Laylee will be available for PC, Mac, Linux, PS4, Xbox One and Wii U, while any Rare game is expected to be an exclusive.