I think because the space is so symmetrical already, it accentuates the uncentered rug. How about a potted Ficus tree or something with more vertical height to take the eye up, off ground level. Or maybe a tall, narrow bookcase.?

I agree..the room is very symmetrical.. There is hardly any space between the couch and the wall..the end Table is pretty skinny..this room is very hard to work with..I had to hire a home decorator and normally I would never do that..there is a fire place in the middle of the room and a door between the windows..I originally wanted a sectional but it wouldn't fit

Can you move the rug a bit to the lefts side of room?

That's what I did with my off-center room. On one side of the couch is a side table with a table lamp and on the other side is a pole lamp.

You could move the rug over and then you would work on visually balancing the room through proper weighting of tables, accessories and lamps rather than relying on symmetry.

No need to center the rug in the room, instead, place the sofa where you want it and center the rug on the sofa. I would definitively keep both side tables and lamps.

I would pull the tables forward, closer to the front of the sofa. Those tables are there to serve the people sitting on the sofa.