While the game was announced during Sony's E3 press conference in June 2011, when Levine said it's "its own thing being built from the ground up", development has yet to begin.
He told IGN: "That's out of my hands right now, that's with the business guys negotiating that business deal and trying to make it work for both sides.
"I've got my fingers crossed that that's going to happen because it's something I want to do but until somebody starts signing the cheques, there's nothing I can do... Hopefully it will come to fruition."
Levine said in October 2011 that Irrational could "potentially" outsource development of BioShock Vita, but only if the studio can ensure it'll still hit the quality mark the series is know for.
Irrational Games has announced that it's already begun development of BioShock Infinite DLC. The firm plans to launch three game add-ons, which will be available for a discounted price as part of the BioShock Infinite season pass.
Publisher Take-Two has confirmed a BioShock Infinite release date of March 26.