If the South African retailer Raru is to be believed, 2K Games are planning to jump aboard the HD remake train once more after finding commercial success with Borderlands: The Handsome Collection. More specifically their website briefly promoted something called "The Bioshock Collection", before it was removed from the database. The formats listed were PlayStation 4 and Xbox One, with November 27 of this year as the expected release date.
As per the contents no details were listed, but a safe bet is that this is a collection with the three games in the series, Bioshock, Bioshock 2 and Bioshock Infinite, wrapped neatly in one package. That being said, neither 2K Games nor Irrational Games (or what remains of them) has said anything about the collection yet, so we'll have to treat this as an unverified rumour for the time being.