In view of the LHC upgrade for the High Luminosity Phase (HL-LHC), the ATLAS experiment is planning to replace the Inner Detector with an all-Silicon system. The n-in-p bulk technology represents a valid solution for the modules of most of the layers, given the significant radiation hardness of this option and the reduced cost. The large area necessary to instrument the outer layers will demand to tile the sensors, a solution for which the inefficient region at the border of each sensor needs to be reduced to the minimum size. This paper reports on a joint R&D project by the ATLAS LPNHE Paris group and FBK Trento on a novel n-in-p edgeless planar pixel design, based on the deep-trench process available at FTK.