"Claims" are just that, so the answer is yes. No matter what claim you're talking about.
Would that claim be acknowledged by country B? Depends on the power that living being holds over country B, and the benefits the current rulership of country B gets by doing so.
There is no international court that judges cases of international law*, there is no international police that arrests sovereign states who are suspected of committing crimes, and there is no international prison to put these sovereign states. There are however plenty of armies ready to take your stuff if you give them an excuse.
Regarding the second part of the question "is is possible?" that depends on motivation of the acknowledging states. Good motivations are either potential trade profits, or gaining a powerful/influential ally, if these benefits cannot be easily acquired by other means (such as capturing or slaying and then harvesting the creature).
*Yes, there are organs that are called "international court", but I was referring to function, not name. These courts serve as "a multinational arbiter", not as "the international court". And even where these "multinational arbiters" have jurisdiction (due to both parties having signed a contract), a sufficient power imbalance between accuser and accused can still frequently sideline them.