We study high-resolution hydrodynamic simulations of Milky Way type galaxies obtained within the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project, and identify the those that best satisfy observational constraints on the Milky Way total stellar mass, rotation curve, and galaxy shape. Contrary to mock galaxies selected on the basis of their total virial mass, the Milky Way analogues so identified consistently exhibit very similar dark matter profiles inside the solar circle, therefore enabling more accurate predictions for indirect dark matter searches. We find in particular that high resolution simulated haloes satisfying observational constraints exhibit, within the inner few kiloparsecs, dark matter profiles shallower than those required to explain the so-called Fermi GeV excess via dark matter annihilation.