According to a forum thread on neoGAF, access to a Battlefield 4 beta is said to come with the pre-order of the upcoming Medal of Honor Warfighter title. Soon after this was shown, it was removed from public eye.
Now, we're not saying Battlefield 4 isn't in discussion, but I wouldn't expect to hear about it anytime soon. First and foremost, there's still a lot of DLC scheduled for Battlefield 3 and those are set to release for the rest of this year and onward into 2013.
Now you may be skeptical about discussion of a Battlefield 4 beta especially when Battlefield 3 just came out in October. Keep in mind that this isn't the first time we've had discussion of a beta way before the release of a title. I'm sure you remember Ubisoft's Splinter Cell: Conviction. Purchasing that game gave you access to the Ghost Recon Future Soldier Beta. Little did we know that we'd have to wait for the beta for a solid two years. I'd expect something similar with Battlefield 4.
Now, keep in mind that this is just a rumor. The official Battlefield twitter feed stated that this wasn't official, since it wasn't on Battlfield.com; but it was on EA's Origin so that must mean something.