There’s been no official announcement, but South African retailer Raru has listings for something called BioShock Collection on both Xbox One and PlayStation 4.
It looks to have been taken down already but they even mentioned a specific release date of November 27, although no description of what the collection actually contains.
Although a sizeable hit in 2013, BioShock Infinite wasn’t quite as successful as publisher 2K were hoping and the team led by Ken Levine was split up. Although it was always implied that more BioShock games would be made in the future.
The name obviously implies the inclusion of more than one game, perhaps even all three (BioShock, BioShock 2, and BioShock Infinite) but that’s an awful lot of work, even if they’re straight ports, for something that’s due out in two months.
The name could instead refer to the inclusion of the, very substantial, two-part DLC for BioShock Infinite, called Burial At Sea.