Is it possible a post-doc position for a specialist in medicine without PhD?
The organization to ask is the organization that wants to employ you. The name postdoc suggest that a postdoc starts after you became a doctor, but there is often some leeway in interpreting those rules. However, how much leeway depends a lot on the specific country and institution. Even within institutions departments can differ quite a lot in the extend to which they are willing to make use of the leeway offered by the rules set at the higher levels. So the only advise we can give you is to talk to HR department of the university that wants to hire you.