The X-ray source XSS J12270-4859 has been first suggested to be a magnetic cataclysmic variable of Intermediate Polar type on the basis of its optical spectrum and a possible 860 s X-ray periodicity. However further X-ray observations by the Suzaku and XMM-Newton satellites did not confirm this periodicity but show a very peculiar variability, including moderate repetitive flares and numerous absorption dips. These characteristics together with a suspected 4.3 h orbital period would suggest a possible link with the so- called dipping sources, a sub-class of Low-Mass X-ray Binaries (LMXB). Based on the released FERMI catalogues, the source was also found coincident with a very high energy (0.1-300 GeV) VHE source 2FGL J1227.7-4853. The good positional coincidence, together with the lack of any other bright X-ray sources in the field, makes this identification highly probable. However, none of the other standard LMXBs have been so far detected by FERMI. Most galactic VHE sources are associated with rotation-powered pulsars. We present here new results obtained from a 30 ksec high-time resolution XMM observations in January 2011 that confirm the flaring-dipping behaviour and provide upper limits on fast X-ray pulsations. We discuss the possible association of the source with either a microquasar or an accreting rotation powered pulsar.