The magnetic properties of Li_{1-x}Ni_{1+x}O_2 compounds with x ranging between 0.02 and 0.2 are investigated. Magnetization and ac susceptibility measured at temperatures between 2 K and 300 K reveal a high sensitivity to x, the excess Nickel concentration. We introduce a percolation model describing the formation of Ni clusters and use an Ising model to simulate their magnetic properties. Numerical results, obtained by a Monte-Carlo technique, are compared to the experimental data. We show the existence of a critical concentration, x_c = 0.136, locating the Ni percolation threshold. The system is superparamagnetic for x<x_c, while it is ferrimagnetic for x>x_c. The 180 Ni-O-Ni inter-plane super-exchange coupling J_perp simeq -110K is confirmed to be the predominant magnetic interaction. From the low temperature behavior, we find a clear indication of a 90 Ni-O-Ni intra-plane antiferromagnetic interaction $J_parallel simeq -1.5K$ which implies magnetic frustration.
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