The paper starts out from a debate that occurred in Germany in 2015, where interpreters claimed to be able to divine Immanuel Kant’s views of the contemporary refugee crisis. It does not attempt to give a substantive answer to the title question, i.e. it does not try to specify the conclusive extension of cosmopolitan right. In contrast, it outlines the systematic work that would have to be done in order to be able to answer the title question. I start from cosmopolitan right as natural right and ask what kinds of transformations cosmopolitan right would have to undergo to form a legitimate part of public international law, in parallel to Kant’s move from provisional private law to peremptory public law in his Doctrine of Right. For that purpose, I introduce distinctions between trivial and non-trivial transformation, between strong (i.e. property-related) and weak (property-unrelated) transformation, and between transformation based on historically blameworthy and historically blameless action.