I agree with most of the people above that say Sheamus has to lose via MITB cash-in, and that sensibly, this person would be a heel (you could always turn a face heel but since WWE is lacking in faces, I doubt this). This leaves 4-5 people: Ziggler, Barrett, Del Rio, Rhodes, and a slim, slim chance of Sandow. Sandow could get the briefcase, build himself up through SummerSlam, then cash-in during the fall months. However, I think a title change is more imminent than that which leaves the other 4.
I don't think the next champion will be Alberto Del Rio. Not that he is not capable, I just think that WWE does not want to go in this direction. If he does have a 1v1 vs Sheamus at MITB, there is about a .1% chance he wins. Assuming this is the case, I could see MITB opening with this match, then later on the card for the WHC MITB, inserting Del Rio for a second match. Still, I would not see ADR winning just because there needs to be new blood in the Smackdown! main event scene.
There is a possibility that Ziggler wins the MITB (assuming he is in the match); however, I do not see this happening. I am more than ready to see Ziggler in the title picture; however, I don't think MITB is the way of doing it. It definitely seems as if WWE is unsure of where to go with Ziggler's character, thus becoming a "tweener". If Ziggler does win MITB, it would be hard to paint him cashing it in as face, unless he does it the straight-up way. If that's the case then, Sheamus will look "weak" from losing. What I would do would be have Ziggler lose MITB, continue his slow face turn, and after a heel takes the belt off Sheamus, Ziggler would be able to feud with said heel.
Cody Rhodes is someone I could definitely see winning. Though Cody obviously doesn't need much more development, he is like Sandow in that I don't think he quite prime for the relatively "permanent" main event scene. A lot like Bryan was last year. WWE has done a VERY, VERY good job in building Cody and not rushing; I just would not want to see Cody champion by SummerSlam. At the earliest, after a Sheamus match at SummerSlam. I'd say there is a 20% chance of Cody becoming the next champion.
Wade Barrett, if ready to return and I really think he is, has a very strong opportunity to become the next champion. He'll come back and be pushed strongly as a heel, we know he is main event capable, and him and Sheamus will put on some good matches. Quite simple, not much explanation needed.
Someone that I did not mention in my previous list because there is not shot of him competing in MITB is Randy Orton. The only "problem" would be that Orton would have to come back heel. When I say problem, I mean that since WWE lacks faces as mentioned before, losing a big face in Orton would be a critical move (maybe him and Ziggler can "swap" so to speak). Fans and even Orton himself would love to see him back as heel, attack Sheamus at the end of July when his suspension is up, which sets up an easy enough booking at SummerSlam.