EA has announced that EA Access will be free for ten days next month, suspiciously enough during E3. This makes it likely that something will be announced tied to EA Access during Microsoft's press conference.
A reasonable guess is that it is either a major but somewhat older game like Star Wars Battlefront is being added to the vault, or maybe there's a bunch of Xbox 360 classics from the last generation being added, possibly something like the Mass Effect trilogy, that is if the publisher continues to release backwards compatible titles on the service.
Thanks, Cheap Ass Gamer.