I like to think that he is a self-driven guy. He's got a strong sense of self preservation from when he was a kid because of Kenny and when he grew up he realized that he can have a sense of purpose as well (leading humans to freedom). I think he is driven by his burdens alone (his and Erwin's mountains of corpses). Though it is also apparent that he just cared generally for a certain brat and a dead commander.
Throughout the series, Erwin was the one that Levi wanted to protect the most. (That's after he had lost all of his friends to a titan.)
Ackermann could only activate their protective instinct to the person that can shift into a titan, in this case it's Eldian.
So the safe bet is that the host that Levi trying to protect is clearly NOT Kenny, because Kenny is also an Ackermann. And he became strong when he was still a child is because Kenny had made him go through a rough training. They once lived in the unerground, it's a tough live there.
Wait, so who would be Levi's host? Who does he try to protect?
He got his powers when he was real young, so possibly Kenny. However, he still remained badass against the wall of titans and Zeke after Kenny's death, so who!?!
Possibly, himself?
I love me my self-loving KING!