Images of the site of the Type Ic Supernova 2002ap taken before explosion were analysed previously by Smartt et al . ( 2002 ) . We have uncovered new unpublished , archival pre-explosion images from the Canada-France-Hawaii Telescope ( CFHT ) that are vastly superior in depth and image quality . In this paper we present a further search for the progenitor star of this unusual Type Ic supernova . Aligning high-resolution Hubble Space Telescope ( HST ) observations of the supernova itself with the archival CFHT images allowed us to pinpoint the location of the progenitor site on the ground based observations . We find that a source visible in the B and R band pre-explosion images close to the position of the SN is ( 1 ) not coincident with the SN position within the uncertainties of our relative astrometry , and ( 2 ) is still visible \sim 4.7 yrs post explosion in late-time observations taken with the William Herschel Telescope . We therefore conclude that it is not the progenitor of SN 2002ap . We derived absolute limiting magnitudes for the progenitor of M _ { B } \geq -4.2 \pm 0.5 and M _ { R } \geq -5.1 \pm 0.5 . These are the deepest limits yet placed on a Type Ic supernova progenitor . We rule out all massive stars with initial masses greater than 7-8 M _ { \odot } ( the lower mass limit for stars to undergo core collapse ) that have not evolved to become Wolf-Rayet stars . This is consistent with the prediction that Type Ic supernovae should result from the explosions of Wolf-Rayet stars . Comparing our luminosity limits with stellar models of single stars at appropriate metallicity ( Z=0.008 ) and with standard mass loss rates , we find no model that produces a Wolf-Rayet star of low enough mass and luminosity to be classed as a viable progenitor . Models with twice the standard mass loss rates provide possible single star progenitors but all are initially more massive than 30-40 M _ { \odot } . We conclude that any single star progenitor must have experienced at least twice the standard mass loss rates , been initially more massive than 30 - 40 M _ { \odot } and exploded as a W-R star of final mass 10-12 M _ { \odot } . Alternatively a progenitor star of lower initial mass may have evolved in an interacting binary system . Mazzali et al . ( 2002 ) propose such a binary scenario for the progenitor of SN 2002ap in which a star of initial mass 15-20 M _ { \odot } is stripped by its binary companion , becoming a 5 M _ { \odot } Wolf-Rayet star prior to explosion . We constrain any possible binary companion to a main sequence star of \leq 20 M _ { \odot } , a neutron star or a black hole . By combining the pre-explosion limits with the ejecta mass estimates and constraints from X-ray and radio observations we conclude that any binary interaction most likely occurred as Case B mass transfer , either with or without a subsequent common envelope evolution phase .