Lately, some job postings from Respawn Entertainment brought up question marks about the new projects especially for Apex Legends universe. There are other guesses like Titanfall 3 too, but currently there is no sign of it. A Senior Environment Artist post referred to the project as Apex Universe FPS Incubation Title though.
While the Apex universe is mostly focused on competitive side of gaming, a single-player project could be nice in order to dive deeper into the lore and story. This is still an early time for the rumors, but job postings mostly provide glimpses of what is coming.