We report inverse bremsstrahlung (IB) heating rates in the eikonal approximation (EA). The present analysis is performed using the plasma-screened Rogers and Debye potentials for Xe clusters with two different charge states (6 and 10). We compare the eikonal results with the first Born approximation (FBA) and classical-simulation (CL-sim) (Moll et al., Phys. Plasmas 19, 033303 (2012)) calculations for clusters in infrared light. Calculations have been performed for the field strength of 2.6 × 108 V/cm. We find that compared to the FBA and CL-sim methods, the IB heating rate in the EA is less sensitive to the choice of the two potentials considered here. The present EA calculation shows that the influence of the inner structure of atomic ion on the heating rate is more prominent for the smaller ion charge (Xe6+). In the case of low laser field approximation based on the elastic transport cross sections, it is seen that in contrast to the FBA and classical methods, the heating rate predicted by the EA does ...