In this paper, we study the effect of channel estimation error at the receiver on the mutual information of a multi user multiple input multiple output (MIMO) channel obeying Rayleigh fading. We assume that imperfect knowledge of the channel is available at the receiver and find the upper bound and the lower bound on mutual information for Gaussian input signals for the uplink of this system. We prove that when the input power at each user is uniformly distributed over its transmit antennas, the bounds on the mutual information are asymptotically tight for Gaussian input signals and this tightness increases when the number of users increases. Numerical simulations are conducted to corroborate theoretical results.