This work is concerned with the design of a readout chip for application to experiments at the next generation X-ray Free Electron Lasers (FEL). The ASIC, named PixFEL Matrix (PFM2), has been designed in a 65 nm CMOS technology and consists of 32 × 32 pixels. Each cell covers an area of 110 × 110 μm2 and includes a low-noise charge sensitive amplifier (CSA) with dynamic signal compression, a time-variant shaper used to process the preamplifier output signal, a 10-bit successive approximation register (SAR) analog-to-digital converter (ADC) and digital circuitry for channel control and data readout. Two different solutions for the readout channel, based on different versions of the time-variant filter, have been integrated in the chip. Both solutions can be operated in such a way to cope with the high frame rate (exceeding 1 MHz) foreseen for future X-ray FEL machines. The ASIC will be bump bonded to a slim/active edge pixel sensor to form the first demonstrator for the PixFEL X-ray imager. This work has been carried out in the frame of the PixFEL project funded by Istituto Nazionale di Fisica Nucleare (INFN), Italy.