In an interview with Polygon Gearbox Software's Randy Pitchford made it clear no Borderlands 3 development had begun at the studio.
"We are not working on Borderlands 3. That is unqualified. We have more to do in the franchise, but no there isn't a Borderlands 3."
"We love Borderlands, and we know customers do too. So we will be doing more in Borderlands. But the thing that, when you think of what Borderlands 3 should be... No. We are not developing that right now. We don't know what that is yet. We can imagine what it must achieve, but we don't know what it is yet. I'm not going to fuck around with you like Valve does with Half-Life 3. Look. We know we want it and we know it should exist, but we don't know what it is yet. But we are doing things in Borderlands that we'll announce soon, that are good, and that I think people will be really excited about if you love the franchise."
But Gearbox are keeping busy. There are Homeworld remasters and two new unannounced next-gen IPs in the works (presumably one of them is the reworked Furious Four concept).
"We created Brothers in Arms. We created Borderlands. We acquired Duke Nukem. We acquired Homeworld. I'm building two original IPs for next-gen. I can't personally invest myself wholly in all of these things. So I invest myself in one or two things, and empower talent and creativity around me and beside me and in this vicinity. I do whatever I can to fuel that and let awesome people do awesome things. I love that feeling."
Meanwhile, Telltale Games are working on Tales from the Borderlands and Borderlands 2 is coming to PS Vita. Presumably we'll also see more DLC for Borderlands 2.