Respawn CEO Vince Zampella says:
I guess EA announced a sequel, so I could play coy and pretend I don't know anything about it, or… yeah. So we're working on a sequel. No official name yet, but we're working on that. That's the main focus but we're starting up a second team and doing some smaller stuff too. Small, exploratory, taking it slow! It'll be multiplatform.
No release date has been announced. Zampella says the team is still "figuring out" what to do with a single player element, because he doesn't want to isolate players who aren't interested in it, or beat them over the head with it. He also addressed the possibility of free DLC, saying:
I think having the maps [released in paid] packs, splits the community and it makes it harder for matchmaking, it’s messy. I don’t know we won’t do it again, I can’t say that for sure, but the idea would be to do something different.