Uhh... I'm not sure exactly what you're asking.
Do you want to use electricity to turn the compressor and then expand the same air out the nozzle? (Don't need a turbine if you're driving the compressor...) Though this isn't really a jet engine per se.
Do you want to just spin a propeller like on a prop plane?
Do you want to heat the air with heating coils (instead of burning fuel in it)? (Not using combustion as a heat source has been done before--they built nuclear aircraft in the 50s/60s. They = US & USSR.)
All 3 of those would be possible ways to propel an airplane with only electricity. But the low energy density of batteries makes this plan generally pretty bad.
Jet engines run on a very simple principle--something called the "Brayton cycle." Basically, you draw air in through the intake. The air is compressed by the compressor (spinning fan blades); the power to drive the compressor typically comes from the turbine (coming up later). After compression, (atomized) fuel is injected & burned. Then the hot hot hot gasses are expanded through the turbine (which powers the compressor); the turbine only extracts enough energy to drive the compressor (on a big engine, the efficiency of this is really high... like 99%

. It works exactly opposite from the compressor--expanding gasses cause the turbine blades to spin. Energy remaining in the air will be converted to thrust as it is expanded out through the nozzle. (i.e., expanding gasses push against the walls of the engine, producing thrust.)
So if you drive the compression w/electricity, you don't need a turbine. If you heat the air w/electricity, you don't need combustion. But accomplishing either of these tasks on a large scale (like an airliner engine) would be really difficult.