No, I'm not shipping them. Just a few thoughts on what should happen to these two at some point.
Two things, I think, are a must: 1. A conflict that will end with Levi resorting to some discipline training of Mikasa; 2. In general, Levi should train Mikasa.
ATTENTION: This blog will have spoilers that the Manga readers know, so if you're only watching the Anime, be warned! Heavy spoilers!
Even though Mikasa was graded as the perfect soldier by her mentors, we know that she's got a major flaw that couldn't be seen in the training, and that is her motivation for joining the military and priorities. She would throw the whole army to hell if Eren was in any way in danger. Several times she disobeyed direct orders and has acted recklessly, putting not only herself, but her comrades to risk because of her personal feelings.
She has been called out on such behavior several times, but Levi has expressed his displeasure more than anyone else. Every time he did, I was thinking "this is it. This is the moment, he'll beat (figuratively) some sense into her. It will be a nice growth for the character and overall an intense, exciting development of the story!" For some reason it still hasn't happened. Granted, there were moments where Mikasa acknowledged some of her mistakes, but it's just not enough. This is such a letdown, since the conflict has been brewing there for a long time, Levi is a character perfectly positioned for the role but nothing! It's like the author is teasing me showing the perfect opportunity for such a conflict to occur and then dropping it in favour of something else.
Not to mention, the main characters haven't had as much development as some side characters, take Jean for example. I don't expect that Mikasa will one day get over Eren and act like a normal person, I think she's broken beyond that possibility. But that doesn't mean she can't progress to a certain point, she has been shown to care for her friends and comrades ore than once, so she can be taught to give Eren some space and take others in consideration a bit more, at least to a certain degree.
Now don't get me wrong, I don't see Mikasa as a Mary Sue character as so many do. On the contrary, I find her quite complex, but mostly static. She needs to evolve a lot more, all the potential is there, it needs to be used.
Speaking of potential...
Being Ackermann, Mikasa can't find the normal soldier's training challenging, everything they dropped on her she could handle with ease. Sadly this means she could not realize her full potential. Her abilities exceed those of normal humans, but Levi outruns her by miles. 'Course Levi is probably twice her age and he has had a lot more training and loads of experience, but I think the most important factor was him being mentored from a very early age by another Ackermann.
A good training means pushing the boundaries you have and expanding them. Mikasa was never pushed beyond her limits in her training, which means she had limited opportunities to upgrade her skills and hone them to the fullest. If Levi trained her it would be a completely different story, since he would be training her acknowledging that she's a genetically modified super soldier like himself and he'd know how far her limits are better than anyone else.
Let's also not forget that Eldians of Paradis are now aware that there's war coming and they have been preparing for it. They will have to deal with a huge army, technologically more advanced opponent, entire divisions of pure Titans and several Titan shifters. They need to use every strength they can. Levi turned out to be one of their greatest weapons, who could singlehandedly deal with the Beast Titan, and Mikasa could potentially be just as powerful, if sufficiently trained. It makes all the sense in the world for them to try their best to use her potential to it's fullest. And Levi is the only person alive who could train her that way.
In conclusion, putting these two things in the story would give us:
1. Much needed character development for one of the main protagonists;
2. An interesting and exciting conflict between two prominent characters;
3. Balancing out strengths between two factions;
4. A logical continuation of both the overall plot and the relationship between these two characters;
5. A good excuse to temporarily concentrate on two of the top most popular characters aka justified fan service;
6. Lots of kickass action and pure badassary!
Tell me what you think :)