ZeniMax has posted a range of new job vacancies on their jobs page which has sparked a lot of new rumours. Based on the job listings, it’s clear that Id Software is hiring people for a new project relating to “an iconic action FPS” series. This has led to a lot of suggestion and hope it might be related to Quake.
One of the job listings is for an Environment Concept Artist (https://jobs.zenimax.com/requisitions/view/2173) which openly states the role is for a team relating to the “development of a long-running iconic Action FPS”. The listing for a Senior Technical Animator/Character TD (https://jobs.zenimax.com/requisitions/view/2307) also mentions the applicant will work on a “long-running iconic action FPS”. Other listings also reference “sci-fi and fantasy environments” which would certainly fit the style of the Quake series.
There’s no way to know if Id Software is working on a new Quake game or a remaster considering the second game will be 25 years old next year. Hopefully there will be some kind of announcement about this n the future but we’re unlikely to hear a new Quake game being announced outside of E3 or QuakeCon.