It would probably be helpful if you posted a photo shot from farther back so more of your room can be seen :)

Added some more pictures at different angles

Many rug websites have tools where you can upload your photo and the site will insert a rug.

What exactly do you mean by modern? Do you have any inspiration photos? Would you like to add some color to the space? Right now your room looks more transitional than modern.

https://www.rugs-direct.com/

Here are photos of rugs on gray flooring. Any one of these rugs would work. I would choose a light tone with some pattern color in it but you may do otherwise. Like I said, any one of them would work. https://www.google.com/search?channel=mac_bm&source=univ&tbm=isch&q=wayfair+light+print+rug+to+go+with+gray+wood+flooring&client=safari&sa=X&ved=2ahUKEwiv1N6bldjuAhUQU98KHf4RAUYQ7Al6BAgDEA8&biw=1366&bih=666

This is a modern medallion rug I think compliments both warm and cool tones in your room, and contrasts nicely with your gray floors:

https://rugs.com/beige-8x11-dahlia-area-rug-6280238?pos=10&rt=aisle

The mock-up skews the color (it’s not actually this yellow hued) and pattern size a bit, but to get an idea.

ETA: I took so long posting, didn’t see the good ideas above. So many choices available for the color scheme and style of your room.

Thank you I decided on the modern medallion

Good choice, the blue will be a pretty accent color for your room.