This company has a selection of rugs, some of which are similar: https://www.overstock.com/Home-Garden/Area-Rugs/Flatweave,/weave-type,/244/cat.html

Here are some kind of similar ones Danny Gray https://www.allmodern.com/rugs/pdp/danny-grayivory-area-rug-mtna1779.htmlDanny  https://www.allmodern.com/rugs/pdp/roxanne-hand-knotted-wool-creambrown-area-rug-cstd6420.html

I know they use antique rugs in some designs, this may be one, too, otherwise I’m guessing it’s a designer rug they sourced through the trade. Horchow does have some in a similar style.

If large, rug size should be big enough for front feet of all seating to be resting on it, which doesn’t look possible with layout. Other option is to place a smaller rug in front of couch and to make it feel less awkward, add a coffee table. Suggest taping out different sizes to experiment. Rug colors in other rooms don’t have to be the same but your room‘s shades need to be pulled together, so I’d use a rug similar to one in picture and then add complimentary cushions.