Safe screening rules are powerful tools to accelerate iterative solvers in sparse regression problems. They allow early identification of inactive coordinates (i.e., those not belonging to the support of the solution) which can thus be screened out in the course of iterations. In this paper, we extend the GAP Safe screening rule to the L1-regularized Kullback-Leibler divergence which does not fulfill the regularity assumptions made in previous works. The proposed approach is experimentally validated on synthetic and real count data sets.