A region of zero current density in the plasma centre has been observed in the advanced tokamak scenarios with off-axis Lower-Hybrid current drive in the JET and JT-60U tokamak experiments. Significantly, the central current density does not become negative although this is expected based on conventional current diffusion. In this paper, it is shown that the zero central current density and the absence of negative central current can be explained by the influence of a resistive kink magnetohydrodynamic instability.