Its impossible to answer your question accurately because you have not provided enough information. The answer can be anything from a few hours to a few months depending on where you are at in your medical treatment, how big the claim is, what insurance company is involved etc.. Contact a workers compensation attorney near you and be prepared to bring any medical records and other documents from the insurance company to get an accurate answer.
Of course the insurance company will settle your case today if they know you are not represented and don't know how to properly value the case. They have the advantage of doing this every day, and you don't.
As my colleague has noted, it is like asking how long it takes to build a boat. Is the boat a canoe or an ocean liner? Is the case dispute? Are your deficits agreed? is your medical care completed? Will you need more medical care in the future? Are all of your medical bills paid?
These and other questions determine how long the process will take. You are likely to do better with an attorney in most systems. Make any attorney explain how they could add value to your case. Good luck.
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Some workers comp cases take years to settle primarily because these types of claims are about making sure the injured worker gets the proper medical treatment and/or job training to return to the workforce. In some cases where it appears obvious that the person is permanently disabled a "lump sum" settlement is appropriate.
Don't forget to check "Helpful" if I helped you out. This response is not intended to create an attorney client relationship and is based on the limited information available at the time of the response. Before acting on anything stated or referenced in this response you should consult with an attorney of your choosing and go over the specific details of your legal circumstances. My responses are also given in the context of the laws of the State of Louisiana. To the extent this comment involves principles of law governed by another state my comment merely reflects my opinion and should not be considered legal advice.
My colleagues have already provided you with some employers. The only thing I would add is that, at least in Louisiana, although most workers' compensation claims ultimately settle, some never do. That's because an injured worker cannot force the employer/insurance company to settle their claim, and likewise, the insurer can't ever force an injured worker to settle.
Also, the employer has to approve of/agree to any settlement, and sometimes, they refuse to. Consequently, some claims will never settle, even if the claimant and insurer are both able to agree to terms.
I would recommend that you consult with an experienced workers' compensation attorney in your area. If your claim can be settled, an experienced attorney will be able to recover far more for you, after their fee, than you will be able to recover on your own. Good luck!