How to manufacture a cable ?

It depends upon how many you are ordering at a time.

Be very knowledgeable about intellectual property laws, or lack thereof, in countries where you might be considering manufacturers for your cables.

Just out of curiosity what type of initial run are you looking at. If it's a small t5o moderate amount I might know someone who can help you.

I am talking more about the manufacturing process.
If I decide to subcontract, where do I find a good one ?

There's New England Wire, Calmont and Bay Associates just to name a few. Might also want to talk to Hal Marker at HM Wire. He can be a very good resource.

Is there a good Chinese cable company I could contact, to bring down the cost ?

What, we don't have enough offshoring being done already?

If it is a cable DESIGN you are talking about I would try to find commercially available wire to use. It is fairly easy to make cables in your basement if the ingredients can be obtained off the shelf. I recently purchased a very good arm cable made by an enthusiast who started making them for his own use and found there was a demand for them. Having wire made up to your specifications is going to be a much more difficult proposition and few of the commercial cable companies actually make their own. Making anything complex in small quantities is always expensive, things like Cardas or Siltech are quite complex.