It sounds like 2K Games' dormant BioShock series could be making a long overdue comeback soon, with a so-called "top-secret studio" now working on an unannounced new entry in the series. According the Kotaku's report, the studio and individual devs were hit hard when they lost out on bonuses, which were contingent on Mafia III getting either an 80 or 85 on Metacritic (it ended up with a score in the 60s).
A "top-secret" studio is working on the next BioShock game, and it's now being developed under the codename Parkside.
According to Mafia 3 developer Hangar 13, a new BioShock title is in the works at a top-secret studio at 2K Games.
Whilst the following is a stretch, signs are pointing at the secret studio being made up of Hanger 13 and BioShock-affiliated 2K Marin members. "It was all very tight-lipped". He claims that a new BioShock is in development at a "top-secret" 2K studio located in the San Francisco Bay area.
However, it wasn't as easy as just bringing Hangar 13 employees over to work on BioShock. Since then, there have been some re-releases and remasters for current-generation consoles, but nothing substantial in the way of a new game.
No other mention of a new BioShock is contained within the article and we can find no other mention of such a title from other sources. While many are leaning towards it being Borderlands 3, it could be the new BioShock, because the franchise is really important to the company. Presumably that means Ken Levine won't be involved in the project, as he's now working on an original project at his new 2K-backed studio Ghost Story Games. However, a hand full setup shop in the studio next door and is supposedly working on a yet to be announced BioShock game. This is because a 2K studio of some kind is now working on the game as we speak. What little evidence is available at present though, seems to point in that direction.