Usually would want either the wall or the rug to be a solid color, especially if the rug is to be a large or room sized rug; however, if you're choosing a rug with two shades of the same color and that color or those colors are in the wallpaper, that could work. With that wall paper, you might consider a muted shade of green for your rug.
However, and this would be my preference, IF this is a lady's room and IF the lady likes pink, you might consider a smaller, elongated oval braided rug for beneath the wing back chair (and a very small foot stool) with a muted pink in it, perhaps with a beige/tan color of the adjoining wall or even a pale neutral gray. If there are other colors, as long as they are muted colors or the overall effect of the mix of colors is a muted effect so they compliment and work with the wall paper rather than compete with it for attention.
This could work by or beneath the chair:
https://www.overstock.com/Home-Garden/Safavieh-Hand-woven-Reversible-Red-Green-Braided-Rug-5-X-8/6688763/product.html?option=8040980
https://www.overstock.com/Home-Garden/Area-Rugs/31446/subcat.html?featuredproduct=14195282&featuredoption=31429647&kid=9553000357392&ci_src=17588969&ci_sku=20791279-000-029&cnc=US&cid=248963&type=pla&targetid=pla-538765374880&track=pspla&gclid=EAIaIQobChMImM3muKnB7AIVibWzCh1-LwyKEAQYASABEgJayvD_BwE
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