Croteam has stated on their forum that Serious Sam 3: BFE [Steam] running on their new Fusion engine which uses Vulkan could arrive in public Beta as early as next month.
From their forum post:
Quote[..]There are no official deadlines, but my hope is that Fusion version of SS3 would enter public beta in the next month or so.
For those that don't remember, Croteam are updating all of the Serious Sam games to their new "Fusion" game engine. This newer game engine will be using Vulkan and it sounds like a big win for Linux, as all the Serious Sam games will support Linux thanks to this.
Thanks for the link mphuZ93.