We have started a new deep , multi-imaging survey of the Fornax cluster , dubbed Fornax Deep Survey ( FDS ) , at the VLT Survey Telescope . In this paper we present the deep photometry inside two square degrees around the bright galaxy NGCÂ 1399 in the core of the cluster . We found that the core of the Fornax cluster is characterised by a very extended and diffuse envelope surrounding the luminous galaxy NGCÂ 1399 : we map the surface brightness out to 33Â arcmin ( \sim 192 Â kpc ) from the galaxy center and down to \mu _ { g } \sim 31 Â mag arcsec ^ { -2 } in the g band . The deep photometry allows us to detect a faint stellar bridge in the intracluster region on the west side of NGCÂ 1399 and towards NGCÂ 1387 . By analyzing the integrated colors of this feature , we argue that it could be due to the ongoing interaction between the two galaxies , where the outer envelope of NGCÂ 1387 on its east side is stripped away . By fitting the light profile , we found that it exists a physical break radius in the total light distribution at R = 10 Â arcmin ( \sim 58 Â kpc ) that sets the transition region between the bright central galaxy and the outer exponential stellar halo . We discuss the main implications of this work on the build-up of the stellar halo at the center of the Fornax cluster . By comparing with the numerical simulations of the stellar halo formation for the most massive BCGs ( i.e . 13 < \log M _ { 200 } / M _ { \odot } < 14 ) , we find that the observed stellar halo mass fraction is consistent with a halo formed through the multiple accretion of progenitors with stellar mass in the range 10 ^ { 8 } -10 ^ { 11 } Â M _ { \odot } . This might suggest that the halo of NGCÂ 1399 has also gone through a major merging event . The absence of a significant number of luminous stellar streams and tidal tails out to 192Â kpc suggests that the epoch of this strong interaction goes back to an early formation epoch . Therefore , differently from the Virgo cluster , the extended stellar halo around NGCÂ 1399 is characterised by a more diffuse and well-mixed component , including the ICL .