Future large high-luminosity electron-positron collid- ers such as Circular Electron Position Collider (CEPC), and Future Circular Collider (FCC-ee) require nanometre-sized beams at the interaction point (IP). The luminosity is very sensitive to the beam orbit drifts at the IP. It is essential to have a fast luminosity feedback system at the IP to maintain optimum beam collision conditions and prevent a luminosity degradation due to orbit drifts in the presence of mechanical vibrations and dynamical imperfections.We considered two possible methods for this purpose for CEPC: one based on measurements of the luminosity and the other based on measurements of the beam orbits around the IP. In this paper, we present the preliminary design consideration for a fast luminosity feedback system at the IP of CEPC.