While Nintendo has yet to officially announce anything, it seems that a listing on Amazon Germany has revealed that the game will be around 6.75GB in size if you were to download it. Like we said the Switch has 32GB of memory by default, so you should be able to squeeze Mario Kart 8 Deluxe in no problem, although if you do have other games then it could be a tight fit.
According to the folks at Nintendo Life, the Wii U version along with its DLCs and update data adds up to about 6.2GB, which means that Nintendo has actually done a good job of keeping the file sizes roughly similar, especially with the addition of the new Battle Mode content. Mario Kart 8 Deluxe will be launched on the 28th of April, 2017 where it will come with all the DLCs included in the previous Mario Kart 8 for the Wii U.