BioShock is one of the most unique game series of all time. The first game was developed under the direction of Ken Levine (Thief: The Dark Project, System Shock 2, and released by 2K Games in 2007 to instantly become a classic beloved by critics and players alike. BioShock 2: Sea of Dreams, developed by 2K Marin, was released three years later and continued the series' winning streak.
The third, and also last BioShock game came out in 2013. BioShock: Infnite, known for a long time as mysterious Project Icarus, was once again made by the Irrational Games (former 2K Boston) and Ken Levine tandem. Infinite till this day is a well-known object of controversy and fans of the series still speculate about the game's sudden ending. Right after Infinite's debut, 2K put the series on hiatus.
According to Kotaku's Jason Schreier, the fourth installment of the BioShock franchise is currently in development. In his long and detailed article about the rise and fall of Hangar 13, the developer responsible for the hated Mafia III, we can read that "many of the people who helped make Mafia III are now gone, including the game’s art director, technical art director, senior producers, design director, many design leads, and a number of other key staff. Some left voluntarily; others were let go or asked to move."
Here's the most important fragment of Schreier's essay: "Some went to other game companies; others moved to the top-secret studio next door to work on an unannounced new BioShock game." The "top-secret studio next door" part presumably refers to 2K Marin, the developer of BioShock 2's single-player mode. Just like Hangar 13, Marin is located in Novato, California, which makes perfect sense.
In May 2014, Take-Two Interactive's chairman and chief executive officer, Strauss Zelnick, stated that 2K Marin was still alive after the mediocre sales of The Bureau: XCOM Declassified, which was released in 2013. At the time, Zelnick also said that "2K Marin will be responsible for shepherding going forward. I don't want to say much else except to agree with you. I think there's a lot of upside in that franchise, , and that future BioShock games would be developed at that facility."
Considering that 2K Marin's last game, The Bureau was released five years ago, there's a big chance the publisher will announce BioShock at this year's E3 in June. Let's also not forget that 2K Marin had been hit with massive staff reductions after the reception of the X-Com spin-off and supporting the studio with the devs of Mafia III would definitely help them in producing a potential next journey to Rapture.