Providing a computer program product, system, and method for setting copy permissions for target data in a copy relationship. Source data is copied from a first storage to a first data copy in a second storage. A request is received to copy requested data from the first data copy to a second data copy. The second copy operation is performed to copy the requested first data copy form the second storage to a second data copy in response to determining that the requested first data copy is not in the state that does not permit the copying. The request is denied in response to determining that the requested first data copy is in the state that does not permit copying.