In this paper,we perform a numerical integration of 666 fictitious binary Centaurs coming from the trans Neptunian space. Our population is restricted to tight binaries whose components have sizes between 30 and 100 km. We included the dynamical perturbations from the giant planets, Kozai Cycles induced by the Sun and tidal friction on the orbits of the binaries. We found that most binaries are disrupted during one of the close planetary encounters, making the mean lifetime of binary Centaurs much shorter than the one of single Centaurs. Nearly 10 per cent of the binaries reach a very tight circular orbit, arguing in favour of the existence of a non-negligible population of contact Centaurs. Another 10 per cent survive as a binary during their lifetime as Centaur. Our simulations favour the existence of a small population of very tight binary Centaurs.