We study the influence of Gribov copies, in the Landau gauge, on the lattice renormalisation constant ZA of the axial current, obtained from a Ward identity on quark state correlation functions, with the Clover action, in quenched SU(3) gauge theory. A comparison between the gauge invariant determination of ZA and the gauge dependent one is discussed. On a 16 3×32 lattice at β=6.0 and with K = 0.1425, the values, on a sample of 36 configurations, are ZA=1.08(5) (gauge dependent calculation) and ZA=1.06(2) (gauge independent calculation). We find that the residual gauge freedom associated to Gribov copies induces observable effects, which, at the level of numerical accuracy of our simulation, are included in the statistical uncertainty inherent in a Monte Carlo simulation. Doubling the statistics suggests that the fluctuation due to the lattice Gribov ambiguity scales down at least as fast as a pure statistical error.