A search for cosmic neutrino sources using six years of data collected by the ANTARES neutrino telescope has been performed . Clusters of muon neutrinos over the expected atmospheric background have been looked for . No clear signal has been found . The most signal-like accumulation of events is located at equatorial coordinates RA= - 46.8 ^ { \circ } and Dec= - 64.9 ^ { \circ } and corresponds to a 2.2 \sigma background fluctuation . In addition , upper limits on the flux normalization of an E ^ { -2 } muon neutrino energy spectrum have been set for 50 pre-selected astrophysical objects . Finally , motivated by an accumulation of 7 events relatively close to the Galactic Centre in the recently reported neutrino sample of the IceCube telescope , a search for point sources in a broad region around this accumulation has been carried out . No indication of a neutrino signal has been found in the ANTARES data and upper limits on the flux normalization of an E ^ { -2 } energy spectrum of neutrinos from point sources in that region have been set . The 90 % confidence level upper limits on the muon neutrino flux normalization vary between 3.5 and 5.1 \times 10 ^ { -8 } GeV cm ^ { -2 } s ^ { -1 } , depending on the exact location of the source .