Banjo-Kazooie’s last appearance on a Nintendo platform was in 2005’s Banjo-Pilot racing game for the Gameboy Advance, published by the former THQ. This was after Microsoft acquired Rare in 2002, but did not have a stake in portable gaming, freeing Rare to develop the title. With all the talk being about the upcoming Super Smash Bros. title for Nintendo Switch, the question was raised to Xbox head honcho, Phil Spencer:
Yep.
— Phil Spencer (@XboxP3) March 20, 2018
Spencer was asked about this back when Super Smash Bros. for Wii U and Nintendo 3DS announced their DLC poll in 2015, and his response was positive there as well, stating that he would like the idea of Nintendo having Banjo as DLC and that they have “worked with Nintendo on Rare IP before [with] no issues.”
Nintendo has featured other franchises in Super Smash Bros., having characters like Solid Snake from Metal Gear, Sonic the Hedgehog, Bayonetta, Cloud Strife from Final Fantasy VII, as well as Capcom’s Megaman and Ryu, so Banjo may not be out of the question.
Despite all of this, Spencer’s willingness doesn’t increase the chances of Banjo heading to Nintendo’s new game. However, considering that Banjo-Kazooie originated on the Nintendo 64, the possibility is probably higher than people would expect.