Fnn Juhl Desk Chair Fabric Suggestions  

I don't know who the designer is but that's Kvadrat "Hallingdal" on there now. Hallingdal is still produced and you can get that exact colorway or any one of of a lot of others. Maharam is the US distributor and they will send you swatches.
It is a bit scratchy---not a big deal for me except in summer when I only have one layer on. But not everyone is bothered by wool. There are some other Danish fabrics that would be very nice. Do a search of the name Kvadrat on the Maharam site and go for the wools that have been in production since the 60s.
http://maharam.com/products/hallingdal-by-kvadrat/colors/270

Hallingdal, Hallingdal, or Hallingdal. Perhaps not in brown.

Well if it's in his house, that's a pretty good indication that the chair was designed by FJ:
http://design-milk.com/finn-juhls-house/
The furniture index listing shows two different caster styles used for this chair:
https://aleph-01.kb.dk/F/H65KJUDTY5C2BCV56HD8MN2VKXMQLXXX6SI4I57U33QMTC9...
You may also be interested in reading Per H Hansen's book about his house.
Also the chair looks fine, as is, to me.

@Spanky Thanks for the link, I am not bothered by wool either and love the look of the Hallingdal.
@cdsilva Awesome info! The reason I was considering having it reupholstered is there was a lot of foam dust all over it and the foam in the backrest seems to be disintegrating. There is also some staining. However after giving it a thorough vacuuming when I got it home it is in pretty decent shape. Any tips on cleaning? Sorry I am new to all of this.

It looks like the foam in the seat is lumpy from drying out, too? Or is that just an illusion?
Vacuuming the foam dust will help in the very short term but if the foam is drying out and crumbling, it will just keep producing dust every time you sit in it. There are those worn spots on the front corners of the arms, too--I dunno about you but that's a little too much fabric patina for me!
If you decide to reupholster, consider using latex foam in the seat at least---it is divinely comfortable and of course totally appropriate for this chair.

Here is a catalog page for it. Finn Juhl designed the chair. There is a coordinating table. It is model 210, which swivels, tilts, and is height adjustable. The same design chair was available as model 212 without the tilt. It was called the "Technocrat Group."
I am not sure of the precise date of the catalog. It is not early France and Søn. My guess is mid 1960s, but possibly late 1960s could be the case as well.

Yes @spanky, the seat is a bit lumpy, and thanks for the suggestion of latex foam I will look into it. Going to get a quote from an upholsterer I know and see what he says. Do you guys think the piece is worth putting the money into? Would hate to invest more than its worth ya know?

@leif ericson so cool to see the original catalog post! In the link @cdsilva posted it says the design was from 1965. Now I just have to find the table haha.

Just went through my copy of "Finn Juhl and his House", and this chair does not make an appearance (nor does the whole built-in linear desk/table. So while the book is indeed a good read, don't buy it just to see the desk chair.