In this paper we present the first results from an on-going serendipitous survey aiming to identify X-ray selected ‘ normal ’ galaxies ( i.e . not AGN dominated ) by combining archival XMM- Newton data with the Sloan Digital Sky Survey . In the first 4.5 deg ^ { 2 } of this program we have identified a total of 11 ‘ normal ’ galaxy candidates ( 8 of them with optical spectroscopy ) with fluxes f _ { X } ( 0.5 - 8 keV ) \approx 10 ^ { -15 } -10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } . These sources are selected to have low X-ray–to–optical flux ratio ( \log f _ { X } / f _ { opt } \la - 2 ) , soft X-ray spectral properties and optical spectra , when available , consistent with the presence of a stellar ionising continuum . These sources comprise both early and late type systems at redshifts z \la 0.2 with luminosities L _ { X } ( 0.5 - 8 keV ) \approx 10 ^ { 39 } -10 ^ { 42 } erg s ^ { -1 } . This dataset provides the first tight constraint on the surface density of X-ray selected ‘ normal ’ galaxies at relatively bright fluxes spanning two orders of magnitude ( 10 ^ { -15 } -10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } ) . The slope of the ‘ normal ’ galaxy \log N - \log S in the above flux range is estimated -1.4 \pm 0.3 consistent with the euclidean prediction . We also discuss the prospects of ‘ normal ’ galaxy studies at X-ray wavelengths using both our continuously expanding survey and future X-ray missions .