In the core of the Fornax cluster, on the West side of NGC1399, we have detected a previously unknown region of intra-cluster light (ICL). It is made up by several faint ($mu_r simeq 28 - 29$~mag/arcsec$^2$) {it patches} of diffuse light. The bulk of the ICL is located in between the three bright galaxies in the core, NGC1387, NGC1379 and NGC1381, at $10leq R leq40$~arcmin ($sim 58 - 230$~kpc) from the central galaxy NGC~1399. We show that the ICL is the counterpart in the diffuse light of the known over-density in the population of blue globular clusters (GCs). The total g-band luminosity of the ICL is $L_gsimeq 8.3 times 10^{9}$ $L_{odot}$, which is $sim5%$ of the total luminosity of NGC1399. This is consistent with the fraction of the blue GCs in the same region of the cluster. The ICL has $g-r sim 0.7$~mag, which is similar to the colors in the halo of the bright galaxies in the cluster core. The new findings were compared with theoretical predictions for the ICL formation and they support a scenario in which the intra-cluster population detected in the core of the Fornax cluster is build up by the tidal stripping of material (stars and GCs) from galaxy outskirts in a close passage with the cD. Moreover, the diffuse form of the ICL and its location close to the core of the cluster is expected in a dynamically evolved cluster as Fornax.
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