The only way to absolutely guarantee that your headphones don't get chewed on is to place them in a container that the cats cannot open.
Do not assume that just because the container is difficult to imagine opening by a cat that it will be impossible (or even difficult).
I have seen cats knock things off the counter just to break open a container.
You can find a lot of example videos of cats opening things they shouldn't be able to: Cat opens door with round doorknob
Find a hardened container with multiple catches to prevent the cat from getting to your headphones.
Add foam to keep the headphones from rattling around inside.
lifehacks.stackexchange.com/users/10/Adam Zuckerman
Dab hot sauce onto the headphones, not the part that goes in the ear!
lifehacks.stackexchange.com/users/9624/k-l
You could sew a fabric casing for the cord part of your headphones.
I've had cats that liked to chew on rubber/plastic cords (including electrical cords!), and the best solution I found was to make little fabric casings for the cords.
It can be very thin fabric, because the purpose of the fabric is to change the texture to make it less attractive, not to be an impenetrable barrier.
A thin flannel would be good; comfortable on your face, but icky on the cat's tongue.
lifehacks.stackexchange.com/users/4902/mhwombat
Building on the idea of Adam Zuckerman regarding casing of sorts, I would like to draw your attention to earbud cases (as from a google search).
These has loads of variations, but most of them should solve your problem.
Some manufacturers sell the earbuds with decent casings, and it is worth it to look for one of those sets.
Cases comes in multiple variants; closed cases, case where you twist the leads into the case, or open variants where the headphone wires are still somewhat available to the cat.
Note that also ordinary headphones can come with decent casings, and some of these headphones are collapsable before you enclose them in the casing.
lifehacks.stackexchange.com/users/4490/holroy
I had to change my behavior in order to keep my cats from chewing my headphones.
I made it a point to put my headphones up on a hook that my cats cannot access without my holding them up.
There is not much you can do to change the instinct your cats have for chasing after string-like objects, so you should change your behavior to make the headphones less available.
lifehacks.stackexchange.com/users/9494/user70848
You could either place them somewhere high up or in a closet.
Unless your cats are ninja cyborgs from the future, I doubt they can open a closet door (or drawer or other aperture of similar use).
lifehacks.stackexchange.com/users/2775/Demisemihemidemisemiquaver
How can I prevent my cats from chewing up my headphones? I've gone through two sets of earbuds recently and don't want to keep having to buy new ones regularly.  Solutions that involve buying a particular type of headphones are okay--I need to buy another new pair anyway.
How to stop cats from chewing my headphones?
lifehacks.stackexchange.com
<headphones><pets>
lifehacks.stackexchange.com/questions/9748
lifehacks.stackexchange.com/users/8021/Gwen
The only way to guarantee that your headphones won't get chewed is to keep them in a container that the cats cannot open. However, some other effective solutions include sewing a fabric casing around the cord or keeping your headphones high up where the cats cannot reach them. Many manfucturers also sell cases that might solve this problem. The options are to place them in a cat proof container, sew a case or buy a new case or simply place them out of reach.
Place them in a cat-proof container. Sew a case out of something like flannel. Buy a case for the earphones - or a new set with a case. Place the earphones out of reach of the cats.