I have a wicker set in my living room and I have a house cat that sits on the chair
I think that leather would be best if the cat does not have claws. Otherwise, go with a microfiber and use a static bush to pick up the hairs
You could try Aniline leather, hair slides right off, it is stain and scratch resistant, it is colored only with dye and not with a surface coating of polymer and pigment and less expensive than coated leather. Corduroy is also a hearty resistant fabric.
I have microfiber couches and the cats have showed no interest in scratching them up. They also wear SoftClaws which are small caps on their front claws which prevents them from doing damage in case they do scratch. They sometimes leave tiny marks on the couch with their back claws but if I rub the couch a while with a cloth it goes away (at least if you rub the fibers all in one direction they are not visible). I also use a lint roller on the couch to get rid of fur (I didn't wanna get a gray-white-and beige couch! ;) ) Also get them lots of scratching posts of they are not declawed, then they will not want to scratch on your furniture. My cats have a scratching post in every room and they always use it. I have another couch which has rough fiber fabric - and they do like to scratch on that but it is very old so I don't care. Their claws snag in it and they like that feeling. So I wouldn't get any loosely woven/rough type fabric.
Leather will work. I have two kittens and a sofa, loveseat, recliner, about 10 other chairs/armchairs/barstool that also have leather coverings. I've had the kittens for 3 months now and all the furniture still looks great. They will sit on the sofa if you are on it but it is not their fabric texture of choice. It does not stop them from running and leaping on/off the surface. The leather is so smooth that sometimes they leap but miss and fall to the ground or slip and slide. If you want to be super nice to the kitty, get wool or sheepskin. My bf left my wool coat out on a table while doing work in the closet one time, both kittens decided that coat was their new bed. I had kitty hair all over it.
One way is to place a scratch post in front of the chair for them to use instead of the chair. The kind that is the best and sturdiest is a post wrapped in rope. Also two sided tape placed on the lower fabric will help as they don't like any sticky things on their paws. You can also place a throw on the chair that covers the area she seems to be interested in. Another good thing to have is a squirt bottle with water close at hand. Anytime she starts to do something she is not supposed to do give her a squirt. Cats don't like water and she will soon learn what she can and can't do.
