In dynamic susceptibility contrast perfusion MRI, arterial input function (AIF) measurements using the phase of the MR signal are traditionally performed inside an artery. However, phase-based AIF selection is also feasible in tissue surrounding an artery such as the middle cerebral artery, which runs approximately perpendicular to B(0) since contrast agents also induce local field changes in tissue surrounding the artery. The aim of this study was to investigate whether phase-based AIF selection is better performed in tissue just outside the middle cerebral artery than inside the artery. Additionally, phase-based AIF selection was compared to magnitude-based AIF selection. Both issues were studied theoretically and using numerical simulations, producing results that were validated using phantom experiments. Finally, an in vivo experiment was performed to illustrate the feasibility of phase-based AIF selection. Three main findings are presented: first, phase-based AIF selections are better made in tissue outside the middle cerebral artery, rather than within the middle cerebral artery, since in the latter approach partial-volume effects affect the shape of the estimated AIF. Second, optimal locations for phase-based AIF selection are similar for different clinical dynamic susceptibility contrast MRI sequences. Third, phase-based AIF selection allows more locations in tissue to be chosen that show the correct AIF than does magnitude-based AIF selection.