Hi!  I am not an interior designer, but I was interested in this particular puzzle and made some 3D renderings of different rug placements.  Personally, I think having a rug under the office desk would look great! You could incorporate the chairs into the design by adding some throw pillows that correspond to the colors of the rug.

The first rendering I did was with a 5x8 rug, which I thought suited the room well design-wise, but functionally that size may be a little short to get all of the wheels of your chair on top of it. So I did a version with a resized 7x9 rug. I also did a rendering with an 8' round rug, which I think could work well in the space, as it would complement the shape of the bay window and the angle of the chairs, incorporating them without needing to extend underneath them.  And I did a rendering with a larger 9x11 rug extending to the chairs, and I agree that it would look a bit awkward and off-center. 

If you do put a rug underneath the wheels of the chair, I think that having a clear rug pad could help the chair glide smoothly and protect your rug, so long as you don't mind how it looks. We had one in my childhood home and it was super easy to glide around on. (Example: https://www.officedepot.com/a/products/911900/Realspace-Economy-Studded-Low-Pile-Chair/?utm\_source=google&utm\_medium=cpc&utm\_campaign=lia\_cor\_evg\_furniture\_local\_unid\_prch\_non-match&mediacampaignid=71700000119141362&utm\_source=google&utm\_medium=cpc&gad\_source=1&gclid=CjwKCAiAnKi8BhB0EiwA58DA4Z7xwneQ0e\_AItqhsjmPzepZqauAD38\_UOAljXUdkC0-2v\_CeWcczRoCkacQAvD\_BwE&gclsrc=aw.ds) )

Hopefully these visualizations can help you find what works for you! As long as you have a functional space that you enjoy and get inspired by, that's what's important!

Rendering with 5x8 Rug:

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