The current EU Asylum policy is widely seen as ineffective and unfair. We propose an EU-wide market for tradable quotas on both refugees and asylum-seekers coupled with a matching mechanism linking countries' and migrants' preferences. We show that the proposed system can go a long way towards addressing the shortcomings of the current system. We illustrate this claim using the recent problems regarding relocation faced by the European Relocation from Malta (EUREMA) program.