The Physical Internet (PI) is a novel vision that aims to reshape and improve efficiency of transport and logistics. A game-changing vision is expected to have a profound effect on all actors involved in freight transport systems. However, the concept is still in early stages, and the study of the PI in the context of maritime ports has remained unexplored. With maritime ports considered as key global trade enablers, the proposed research aims to provide insights into possible scenarios for the evolution of ports under the development of the Physical Internet. Firstly, a framework that shows the categorical evolution of ports under the influence of three developing PI characteristics is generated, by means of literature review, interviews with experts and brainstorming sessions. Secondly, a scenario logic approach is used to generate hypothetical futures. Both the framework and the hypothetical futures are then used as input for a Delphi-study in which experts in the field of PI assess the level of development of each of the PI characteristics for the years 2030 and 2040. The results from the questionnaire are used to generate the evolution path of maritime ports through the lenses of the proposed framework, for each scenario. An important finding from the survey is that a governance dimension, which entail a set of rules and protocols for a cooperative, safe and reliable PI environment, can lag behind and delay the development of ports towards "PI ports" in the upcoming years. Also, under the most optimistic scenario, the Physical Internet scales up to the regional level at most by the horizon year 2040, with ports not reaching the level of global hub hyperconnectivity by this period, as per the opinions of the PI experts.