We seek to estimate the average level of MHD turbulence near coronal mass ejection (CME) fronts as they propagate from the Sun to the Earth. We examine the cosmic ray data from the GRAPES-3 tracking muon telescope at Ooty, together with the data from other sources for three well observed Forbush decrease events. Each of these events are associated with frontside halo Coronal Mass Ejections (CMEs) and near-Earth magnetic clouds. In each case, we estimate the magnitude of the Forbush decrease using a simple model for the diffusion of high energy protons through the largely closed field lines enclosing the CME as it expands and propagates from the Sun to the Earth. We use estimates of the cross-field diffusion coefficient $D_{perp}$ derived from published results of extensive Monte Carlo simulations of cosmic rays propagating through turbulent magnetic fields. Our method helps constrain the ratio of energy density in the turbulent magnetic fields to that in the mean magnetic fields near the CME fronts. This ratio is found to be $sim$ 2% for the 11 April 2001 Forbush decrease event, $sim$ 6% for the 20 November 2003 Forbush decrease event and $sim$ 249% for the much more energetic event of 29 October 2003.
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