Rumours of a BioShock Collection for the current generation of consoles have been around for ages, though there’s never been any real work from 2K regarding it. However it does appear that an announcement is imminent as the BioShock Twitter account has just tweeted Welcome To Rapture with a cropped image of a Big Daddy and Little Sister.
Welcome to Rapture! Would you kindly follow @BioShock? pic.twitter.com/f010t1WS0O
— BioShock (@bioshock) June 29, 2016
Alongside that spark of activity a screenshot of the 2K website shows a BioShock The Collection page, though trying to access the link now just takes you to the home page.
If an announcement is coming I wouldn’t be surprised if the release is next year to coincide with BioShock’s 10th anniversary, but 2K may want to hit the Christmas period too.
Source: Lifelower Twitter/BioShock Twitter

Avenger
Yes! The one set of games I’d happily pay for and play, completely remoistened for this gen.
Avenger
*play again