Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion discs, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid metal annulus (Couette flow) is explored by local and global stability analysis. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table‐top apparatus, using easy‐to‐handle metals such as gallium. Practical issues of this proposed experiment are discussed.