In Deep Space Nine Companion (page 3 - if you "search inside" the book with Amazon for "Roddenberry", it's the first match), Rick Berman is quoted as saying:
"I was asked to create and develop a series that would serve as a companion piece to The Next Generation for about a year and a half, and then TNG would go off the air and this new show would continue." recalls Berman. "So I asked Michael Piller to get involved, and we put our heads together. I never had the opportunity to discuss any ideas with Gene [Roddenberry]. This was very close to the end of Gene's life, and he was quite ill at the time. But he knew that we were working on something, and I definitely had his blessing to develop it."
There's no mention of Voyager, but it seems unlikely that they were working on developing that series at the same time that DS9 was being developed.