Joseph H Carens is one of the most prominent academic advocates for Open Borders. He argues that all liberal democratic states should have open borders, and this stand is consistent with liberal democratic principles. As he puts it, his positive case for open borders starts from three basic interrelated assumptions:
First, there is no natural social order. The institutions and practices that govern human beings are ones that human beings have created and can change, at least in principle. Second, in evaluating the moral status of alternative forms of political and social organisation, we must start from the premise that all human beings are of equal moral worth. Third, restrictions on the freedom of human beings require a moral justification. These three assumptions are not just my views. They undergird the claim to moral legitimacy of every contemporary democratic regime.
You can find a useful short version of his argument at: