The construction of nanoporous membranes is of great technological importance for various applications, including catalyst supports, filters for biomolecule purification, environmental remediation and seawater desalination. A major challenge is the scalable fabrication of membranes with the desirable combination of good thermal stability, high selectivity and excellent recyclability. Here we present a self-assembly method for constructing thermally stable, free-standing nanowire membranes that exhibit controlled wetting behaviour ranging from superhydrophilic to superhydrophobic. These membranes can selectively absorb oils up to 20 times the material's weight in preference to water, through a combination of superhydrophobicity and capillary action. Moreover, the nanowires that form the membrane structure can be re-suspended in solutions and subsequently re-form the original paper-like morphology over many cycles. Our results suggest an innovative material that should find practical applications in the removal of organics, particularly in the field of oil spill cleanup.