The answer depends on what you mean by “electromagnetic.”

If the hollow sphere has electric current flowing through it (say, copper coils wound around the outside in a non-random way), then you could conceivably make the electromagnet point the same way as the spherical magnet inside, or in the opposite direction. If the sphere is just passively sitting there, and made of a metal that conducts electricity and can be magnetized, then the spherical magnet inside will magnetize the sphere in the same way that a bar magnet magnetizes the paper clips it picks up to make a chain. This also has a few possibilities:
The material of the hollow sphere can be ferromagnetic (also a permanent magnet). It can be paramagnetic, which is to say that it aligns with external fields like iron filings around a permanent magnet. Finally, some metals (like copper) are diamagnetic, which means that they will actually oppose external fields and instead repel the permanent magnet inside no matter which way it points.

What will happen in each of these cases? I’m assuming here that there’s no gravity, or at least that the electromagnetic forces are much stronger, because otherwise the answer is just that the inner magnet falls down and stays at the bottom.

Case 1: The hollow sphere has wires wound around it to create a magnetic field aligning with the permanent magnet in the middle (this is the sort of thing that comes up in college physics classes). Let’s say this field points up and down. Then, if the spherical magnet is exactly in the middle and the top and bottom walls attract it evenly, then all the forces cancel out and it sits just there. However, this is what physicists call “unstable equilibrium,” and the magnet sits like a ball on top of an anthill: any slight nudge and it rockets toward either the top or bottom (whichever is closer) and sticks, since the force gets stronger the closer the magnets get.

Case 2: Same as Case 1, but instead the wires create a field opposing the permanent magnet (the walls repel it). Now, all the walls repel the magnet, and this seems like a stable equilibrium: the closer the magnet gets to a wall, the stronger the repulsion gets, and it feels an overall force returning it to the center. This is called a restoring force, and it’s analogous to a mass bouncing on a spring or a swinging pendulum. This suggests that the magnet can float in the center. However, any slight nudges in the orientation of the magnet will make it flip around. Even though the system is stable in the position sense, it is unstable in the orientation sense, and we’ll see the behavior of Case 1. Think of it like a ball balancing at the center of a Pringles potato chip – all directions have to be stable for the system to be in stable equilibrium.

Case 3: However, what if, as you say, the magnet is spinning in such a way that the north-south alignment of the magnet is always opposite that of the walls? In the same way that it’s easier to stay balanced on a bike when it moves than to balance when stopped, the rotation of the magnet will actually stabilize the system in the orientation direction. You need some minimum angular momentum to achieve this stability, but you could absolutely levitate the permanent magnet this way. Every one of those kits with a levitating magnet only works because the magnet is shaped like a top and spins to provide stability.

Case 4: The hollow sphere is ferromagnetic. It turns out a ferromagnet is the same as having electric current in a ring around the sphere, so you get the same behavior as Cases 1-3.

Case 5: The hollow sphere is paramagnetic. You will get the same behavior as Case 1, since the magnet is attracted to either the north or south pole induced in the sphere.

Case 6: The hollow sphere is diamagnetic. I left the best for last. You get the same behavior as Case 3 without the spinning, which means that the magnet floats in the middle, repelled by all walls. The orientation direction doesn’t even need to be stabilized this time, since the hollow sphere will oppose the field of the magnet no matter which way it points. However, if you give the magnet some initial spin, it will only keep the component of angular momentum parallel to the field direction, since spin in any other direction makes the north and south poles tumble and reverse the field, which an electrically conductive material will oppose. This comes from something called Lenz’s law: a changing magnetic field will induce an electric field, and if the material supports current, the current will create its own magnetic field to counter the change.