No. The two types of motor are fundamentally different. Combustion engines need transmissions because they produce relatively constant torque (within 50% of max torque). Electric motors on the other hand produce relatively constant power.
This makes total sense when you think about it. An IC engine is powered by explosions; every explosion produces roughly the same force on the piston regardless of speed. You can't get more power without more explosions because you can't cram more air in the cylinder. You can only speed up the engine.
In an electric motor, you can cram as many electrons into the wires as you want. You are only limited by how much heat is generated. Increasing speed increases heat slower than increasing torque, but you can still basically increase either as much as you want.