If you have an object pushing or pulling another object, can you convert that force into electricity without either object moving? If you have an object pushing or pulling another object, is it possible to convert that force into electricity without either object moving?
If so, what possible methods could be used for harvesting the pushing/pulling force, and using it to generate electric current?
If the method of generating electricity results in the pushing/pulling force being reduced (e.g. in order to satisfy thermodynamics), that's OK as long as both objects remain stationary and at least some electrical current is generated.
For example, object A might be firmly anchored to the floor, object B is tethered to object A, and object B pulls on object A via a general input force of some kind (e.g. people pulling on it, or whatever).
Either "pushing" or "pulling" forces could be used, since there are essentially interchangeable using levers etc.
 A: In order to generate electricity work must be done. If you push or pull on an object and it does not move you are not doing any work since work is force times the  distance the object moves  in the direction of the force.
If you’ve been following the comments you may have learned that physical effort does not necessarily produce work. If you push or pull an object and it DOES move you’ve done work as defined by physics. If it doesn’t move you haven’t done work as defined by  physics. You physical effort  will expend calories causing you to breath more rapidly and sweat transferring more heat from your body  and increase your heart rate making it work harder (internal work of your body) but you are not doing external work defined by physics.
Hope this helps 
A: Here is one way that gives you almost what you want.
There are ceramic materials called piezoelectrics which, when sliced into thin slabs and squeezed, produce a small amount of voltage (and almost zero current). If you stacked together a very large array of these "tiles", connected them together in parallel and squeezed them, you could produce several volts and if you are lucky one thousandth of an amp of current for a thousandth of a second or so: a tiny amount of useful power for a huge investment of time and effort. 
Piezoelectric discs like this are handy for making microphones and the little beepers that tell you when your microwave is finished heating up your corn dogs, but they are impractical as power generators. 
Note that these devices do obey the rule cited by Bob D above: when you squeeze a piezoelectric disc, the force you apply (which is significant) must move through a distance (which, because the disc is stiff, will be extremely small) in order to perform work on the disc. The disc then transforms that work into a voltage (which is significant) and a current (which will be extremely small). 
A: If your requirement is so strict so as to not allow a single atom to move, electric current cannot happen (electric current is flowing electrons). So the short answer to this question is "no".
The longer answer: it depends on how strict your "no movement" requirement is (and what you consider to be unacceptable movement).
For example, consider a waterwheel mounted to a dynamo, and anchored in a river. Say you hook up an empty rechargable battery to the dynamo and come back a while later. When you come back, the battery is charged. And the waterwheel, dynamo, and river are where you left them.

*

*In a "big picture" view, there was no movement.

*In a "detail oriented" view, the waterwheel and dynamo's rotor turned (which is movement), and numerous water molecules flowed and collided with the waterwheel paddles, and flowed downstream from the waterwheel (which also is movement).

