Faux fur upholstery fabric  

Are you looking for a faux fur or are you looking for a wool pile fabric?  Faux furs are synthetic.  There are wool fleece fabrics that consist of fluffy wool fiber on a synthetic base fabric, usually knitted.  It looks like sheepskin until you part the wool and see the base fabric.  Wool mattress pads are typically made of this stuff and it's also used for lining slippers, mittens, and sometimes coats.  I'm sure you can get it by the yard from somewhere or other.  It may also be made on a woven base fabric which would be better for upholstery unless you're doing something very curvy.
If you're looking for a synthetic, then I dunno...maybe look for stuff used in better quality fake fur coats?  The last time I looked at stuff like this was at least 20 years ago and at that time the best quality stuff was being made in Germany.  Some of it was really, really nice fabric.  
 

Dear spanky,
Thanks a lot for your exhaustive and helpful reply. Whether it's faux fur or wool pile doesn't matter so much to me as long as I can achieve a certain finish. Perhaps putting "faux fur" in the description was slightly misleading, that's simply what it said in the description of an item that was reupholstered in the style I was looking for. If possible, I'd probably try to go for a natural finish like shaved alpaca, which might be more durable than a synthetic fibre. Thanks again for your kind advice. I really appreciate it.
Kind regards,keaton

I can't really tell from the photo you posted what the look of the pile is...it sort of looks like shorn sheepskin but could also be some other look.  I'm just not sure.
Below is a link to some wool fleece fabric made in Australia.  It has a thorough description of how the fabric is made and good photos, too.  
http://www.woolmark.com/fleece-products
I think the pile in most wool fleece fabrics will eventually felt together a bit so that it looks nubby rather than furry, so that's something to keep in mind.
Alpaca is a premium fiber and will be very pricey if you can find it in a deep pile.  Just so you know.
 

There is a maker in France that does this fabric. Can't remember the name. I'll have to ask. I guess before anyone does exhaustive reseearch though you should say how much you're willing to spend. Last time a designer ordered in fabric like this it was near $500 a yard.

Dear spanky, dear keewee,
Thanks a bunch for both your comments. I forgot to enable the notification function, so it's only now that I'm reading your comments. Apologies for that.
Thanks for the link, spanky. I'm gonna look into it straightaway. Personally I find alpaca a good choice. I know of a NYC dealer who sources a very good quality from Germany, but he was not willing to share his contacts, which I perfectly understand. If any of you knows where to find it, that would be amazing.
Ouch, $500 per yard is very steep, really. I'd be willing to spend up to $300 tops, but any amount beyond that really exceeds my financial scope for this project.
Kind regards and thanks so much for all your input,C.

Here you go-
http://www.gerrys.com.au/product.php?productid=3466
That place sells fabric for making teddy bears.  I don't know how suitable this stuff is for upholstery but i've seen some stuffed animal fabric that would probably work.  Just depends on the weight and fiber content of the backing material.  
The one linked above is $375AU which comes out to around $310/yd in US dollars.  

Cheers, spanky! This one looks really good. Ironically enough, last night I came to the conclusion that probably Hayat did use actual teddy fabric on the sofa. He's got other furnishings upholstered in the same style where he actually indicates to have used teddy fabric. I found this: https://www.christiebears.com/acatalog/Alpaca-Mohair-25mm-Dense-Vanilla-...
And this:  http://www.intercaltg.com/colors/100h-7.html#100-81
They've got pile lengths of about 1cm, 1.5cm and 2.5cm, so now I'm wondering which one will have the best look and feel to it - or come closest to the one shown in the image. 2.5 will have the most plush, but might fade rather quickly - or start looking nubby, as you suggested. 1.5 might be a good compromise, perhaps. 1mm is the most care-free, but is not going to have the finish I'm aiming for.
To come back to something you said above: please forgive my ignorance, but what do you mean by "weight and fiber content of the backing material"? As you probably could have guessed, I'm not quite the expert on fabrics...
Best  regards and thanks again for all your helpful suggestions, spanky. I really appreciate it.

No problem.  I have seen a lot of mohair pile fabric; it is often on a rather loosely woven cotton backing that wouldn't hold up for upholstery use, in my opinion.  Some is on a heavier weight backing, though---heavier threads, more closely woven, just a more sturdy feel.  You should probably get swatches and compare.
Is there some reason you want alpaca over mohair?  I think both are very silky fibers and will not felt.  I don't think they tend to mat, either.  I guess matting is just felting, come to think of it.  Alpaca is softer than mohair but mohair is pretty soft.
I think it's probably easier to find mohair pile fabric than alpaca.  And probalbly in way more colors.

Thanks a lot, I understand what you mean. I'm gonna order some samples. The proof is in the pudding, after all.I wouldn't say I've got a good reason to prefer alpaca. To me it always felt a bit nicer than mohair, but that's probably just in the nuances. Thanks for the insights concerning matting and felting. You're right, it comes down to one and the same thing. I'm curious what the swatches are going to look like. Thanks again for all your input, spanky. Much appreciated.

I know someone in Germany who makes fabrics like this. I can tell you the name if you'd like. Of course it's up to you - how much is your budget. It might not be that cheap...

Hey Dean,
That sounds great, thanks so much. I'd love to get the details, if you're willing to share them. It doesn't hurt to ask, and if s/he would be able to supply exactly what I need, I'm sure I can figure something out with the finances.
In case you don't wanna make the details public, please let me know, and I'm gonna drop you my email address.
Kind regards and thanks again for your help!