It looks like Respawn Entertainment may be working on Titanfall 3, or at least, that's what their latest job openings seem to indicate. A few different people on social media and other websites have pointed out that the company seems to be in the middle of a massive hiring phase, which includes several jobs clearly marked as being for Titanfall. They include a Senior Tech Animator, VFX Artist, Build & Release Manager, and more. You can check out all of the jobs at this link, but in total, they're currently looking at filling 15 positions on the team.
Electronic Arts have made it no secret that they're invested in the Titanfall brand and want to expand the game's universe and the IP in general as best they can. So it would only make sense that we'd eventually see Titanfall 3 get the green light from the powers that be. If they're hiring now, chances are we're looking at a 2020 preview at best, maybe later in the year for a release. But that's based on the idea that they're starting from scratch with new hires and are building a brand new game, rather than just trying to upgrade all the old assets with new mechanics built on top.