What about a warm lighter gray?

[Contemporary Living Room[(https://www.houzz.com/photos/contemporary-living-room-ideas-phbr1-bp~t_718~s_2103) by New York Interior Designers & Decorators Shelly Chung Design

You can get a pattern that as camel in it so it will go, if not match. I'm not talking print, but pattern like a herringbone or a tweed, or a nubby fabric with camel in it, or a small geometric...

"Camel matches nothing!"

is incorrect, as camel matches/goes with plenty.
The problem is that YOU personally don't want those colors! No white, no cream, no dark colors....

Look for a print then that has camel in it.

Oh, I just scrolled to see if you mention wall color, and I see that Annie suggested the same!
What color are your walls?

Go to calico corners and search on fabrics, color gold...you'll find lots of great ideas from solids to textures to stripes to paisleys to geometrics and more...lots goes with camel.

Here is a link that might be useful: calico corners

Francoise, navy was my first thought as well.

Can we see your sofa so that we're all on the same page about your particular camel?

Though I would personally love navy with it it seems you want more neutral than that so I'm with Annie with a subtle patter with camel in it.

Olive green or sage may be neutral enough to go with your camel couch.

Here are some suggestions:

or IKEA chairs