While 2K Games have yet to officially confirm the existence of a BioShock collection, rumors seem to have been given some extra credence after the Brazilian ratings board released information about a title called BioShock: The Collection. The Classificação Indicativa revealed that the title would be released for the PlayStation 3, Xbox One, PC, PlayStation 3 and Xbox 360. This suggests that the collection might not be a fully remastered version of the three titles but rather an upscaled edition.
The BioShock series began in 2007 with the release of BioShock, and was later continued with BioShock 2 and BioShock Infinite. BioShock 2 was a direct sequel to the original game but was developed by 2K Marin and 2K Australia rather than Irrational Games, who returned to the franchise with BioShock Infinity.
In 2014, creator Ken Levine revealed that Irrational Games would close following the release of a final piece of downloadable content, with just a few staff moving with him to a new developer that would concentrate on smaller digital only games. This left the future of the franchise in the hands of publisher 2K Games.
All of the entries were commercial and critical successes and with 2K Games confirming that the series would be returning at some point in the future, a remastered collection could keep up interest in the series until a new title arrives. Many publishers have also done this, with games such as Tomb Raider, Dishonored and Halo all having received updated editions in the run up to new releases.