I don't think a round rug would work. A rectangle is perfect, but you need a much larger size. Push your sofa back toward your kitchen a bit, square up the two chairs, and straighten the side tables so they go on the ends of the sofa facing the TV, and you have room to walk between the sofa and other seating to get into the seating area. The photo below shows positioning with space to walk through.

Chestnut Hill Traditional · More Info

I totally agree with Calidesign. Pull everything out a bit so all the furniture can breathe, there's walking room and then look for a MUCH larger rectangular rug for your space. I like the idea of a rust color as well. Your rug doesn't haven't to be so large that all the legs of each piece of furniture fit on it but at least the front two legs of each piece should. adding a coffee table of some sort might also help your space feel more finished

Love the idea of a sisal rug. Make it much bigger as batson_cassie suggested.

Too much going on in the floor to bring in prints.