ELT laser guide star wavefront sensors are planned to handle an expected amount of data to be overwhelmingly large (1600×1600 pixels at 700 fps). According to the calculations involved, the solutions must consider to run on specialized hardware as Graphical Processing Units (GPUs) or Field Programmable Gate Arrays (FPGAs), among others. In the case of a Shack-Hartmann wavefront sensor is finally selected, the wavefront slopes can be computed using centroid or correlation algorithms. Most of the developments are designed using centroid algorithms, but precision ought to be taken in account too, and then correlation algorithms are really competitive. This paper presents an FPGA-based wavefront slope implementation, capable of handling the sensor output stream in a massively parallel approach, using a correlation algorithm previously tested and compared to the centroid algorithm. Time processing results are shown, and they demonstrate the ability of the FPGA integer arithmetic in the resolution of AO problems. The selected architecture is based in today's commercially available FPGAs which have a very limited amount of internal memory. This limits the dimensions used in our implementation, but this also means that there is a lot of margin to move real-time algorithms from the conventional processors to the future FPGAs, obtaining benefits from its flexibility, speed and intrinsically parallel architecture.