Nintendo's main branch has applied for three GameCube trademarks, according to Japanese Nintendo. The site states that these trademarks are not for "general merchandising," but instead for "purposes including video game program and video game machine."
It should be noted that Nintendo filed for a trademark of the N64 back in May, also reported by Japanese Nintendo. What these trademarks are exactly leading to we can only speculate, but it wouldn't be a stretch to consider that Nintendo is thinking long-term on its Classic Edition line. The NES Classic and SNES Classic are incredible hot sellers, so it would make sense for Nintendo to release a N64 Classic Edition in the near future. The console is just old enough to be consider retro, and it would be a great thing for nostalgic, and new players. Then, a few years down the road, a GameCube Classic would make sense.
The GameCube was not one of Nintendo's biggest sellers. It has only sold a little over 21 million units, and that's lifetime sales, according to Nintendo. Its direct rivals, the PlayStation 2 and Xbox, outsold it, according to a chart at Statista. That doesn't mean the console was bad; in fact, it's quite the contrary. Although the GameCube lacked features its competitors had, it had a wide array of games that have gone down as legacy content. Super Mario Sunshine, The Legend of Zelda: The Wind Waker, and Super Smash Bros. Melee all appeared on the console. Metroid Prime, Pikmin, and Animal Crossing (outside Japan) all got their start on the GameCube. Clearly, many longtime Nintendo fans have fond memories of the console.
The GameCube controller is still immensely popular today, and has become the standard for Super Smash Bros. In fact, all these years later, you'll be able to use the GameCube controller for Super Smash Bros. Ultimate later this year on Switch. That speaks volumes of the legacy of the GameCube. While we don't know the end result of these trademarks, one thing remains certain: Nintendo has not forgotten about the console.
Interestingly, in the same report by Japanese Nintendo, Nintendo has also applied for a trademark for "Game Boy." Now, what could that mean? A Game Boy Classic Edition would certainly be interesting, as the console houses classic titles, such as Pokémon Red and Super Mario Land. But, this is just speculation. The Game Boy is an arguably bigger name than the GameCube, so it makes sense that Nintendo would want to do something with its classic small console. Hopefully we'll learn more details in the near future.