In an October earnings call, Electronic Arts CEO Andrew Wilson made it pretty clear that Respawn is working on not one, but two new games at present. One of those is the studio's forthcoming Star Wars shooter. The other, Tom speculated at the time, could be a new instalment in the Titanfall series. According to a bunch of job listings Respawn has posted, a new Titanfall game seems pretty bloody likely.
The studio has been posting Titanfall related jobs for the better part of the year, and most of them originally appeared long after any new major Titanfall 2 content update (the last, so far as I can see, was in December 2017). Unless Respawn is preparing a doozy of an unexpected Titanfall 2 update, it's safe to say these listings relate to a new game.
The most recent listing was published on December 15, and advertises for a senior technical animator to work on the Titanfall series. The earliest job opening that's still open, dates back to April. Unfortunately, none of these listings specify "Titanfall 3" or even hint at any other solid information about a forthcoming game.
It's usually a non-event when a blockbuster series gets a new instalment, but Titanfall 2's launch didn't exactly set the world alight, especially as EA released it in the shadow of Battlefield 1. Respawn CEO Vince Zampella said the studio was "heavily invested" in the Titanfall universe in mid-2017.